Jesus did tell the Jews in the most certain terms exactly who He is. Keep in mind that Jesus came and preached primarily to the Jews, who had the Scriptures and who, unless already hardened by unbelief, had everything that they needed to recognize His identity as Christ, Messiah, Son of God, and Heir of all things.
Jesus said to them, “If God were your Father, you would love me, for I came from God and I am here. I came not of my own accord, but he sent me. Why do you not understand what I say? It is because you cannot bear to hear my word. You are of your father the devil - John 8:42-44a
His seeming refusal to clearly vocalize His identity is, in itself, an indictment of their preexisting and willful unbelief. His words produced division within the ranks of those He came to save and that division arose from the harmony of His words with His deeds:
There was again a division among the Jews because of these words. Many of them said, “He has a demon, and is insane; why listen to him?” Others said, “These are not the words of one who is oppressed by a demon. Can a demon open the eyes of the blind?” - John 10:19-21
The Jews then demand:
“How long will you keep us in suspense? If you are the Christ, tell us
Jesus' reply is that He has told them and they do not believe and then immediately asserts that the works He is doing in the Father's name bear witness to Him:
Jesus answered them, “I told you, and you do not believe. The works that I do in my Father's name bear witness about me, but you do not believe because you are not among my sheep. - John 10:25-26
However when the High Priest and the council demand, on oath by the living God (Matthew), a direct answer from Jesus he gives them one, plainly telling them that if He answers they will not believe:
If thou be the Christ, tell us.' And he said to them, 'If I may tell you, ye will not believe; and if I also question you , ye will not answer me or send me away;
henceforth, there shall be the Son of Man sitting on the right hand of the power of God.' And they all said, 'Thou, then, art the Son of God?' and he said unto them, 'Ye say it , because I am;' and they said, 'What need yet have we of testimony? for we ourselves did hear it from his mouth.' - Luke 22:67b-71 (YLT)
When Jesus appeals to His works as the basis for their belief this is exactly what He is saying; that the Jews, seeing that He is doing just what the Messiah was prophesied to do, should believe without a personal confession, i.e. that their hearts should have been prepared and receptive rather than hard at His arrival:
If I am not doing the works of my Father, then do not believe me; but if I do them, even though you do not believe me, believe the works, that you may know and understand that the Father is in me and I am in the Father.” - John 10:37-38
This is exactly the answer that He gives to John the Baptist when John expressed doubt and sent his disciples to question Jesus:
“John the Baptist has sent us to you, saying, ‘Are you the one who is to come, or shall we look for another?’” In that hour he healed many people of diseases and plagues and evil spirits, and on many who were blind he bestowed sight. And he answered them, “Go and tell John what you have seen and heard: the blind receive their sight, the lame walk, lepers are cleansed, and the deaf hear, the dead are raised up, the poor have good news preached to them. And blessed is the one who is not offended by me.” - Luke 7:20-23
In answering this way Jesus gently referred John back to Isaiah 35 in order to strengthen John's wavering faith by rooting it, once again, in Scripture. We might think that a simple 'yes' should suffice but the Lord knows that the bread of our faith must be every word that comes from the mouth of God.
And Jesus agonized over the hard hearts of his people:
O Jerusalem, Jerusalem, the city that kills the prophets and stones those who are sent to it! How often would I have gathered your children together as a hen gathers her brood under her wings, and you were not willing! Behold, your house is forsaken. And I tell you, you will not see me until you say, ‘Blessed is he who comes in the name of the Lord!’” - Luke 13:34-35
This is why Jesus marveled out loud at the faith of the Canaanite woman and the Roman centurion and when He announced to the Jews in Nazareth, directly from the Scripture, who He was:
And the scroll of the prophet Isaiah was given to him. He unrolled the scroll and found the place where it was written, “The Spirit of the Lord is upon me, because he has anointed me to proclaim good news to the poor. He has sent me to proclaim liberty to the captives and recovering of sight to the blind, to set at liberty those who are oppressed, to proclaim the year of the Lord's favor.” And he rolled up the scroll and gave it back to the attendant and sat down. And the eyes of all in the synagogue were fixed on him. And he began to say to them, “Today this Scripture has been fulfilled in your hearing.” - Luke 4:17-21
it is why He chastised them so severely for their unbelief. They knew He was indicting them and, rather than repent, they were infuriated.
But in truth, I tell you, there were many widows in Israel in the days of Elijah, when the heavens were shut up three years and six months, and a great famine came over all the land, and Elijah was sent to none of them but only to Zarephath, in the land of Sidon, to a woman who was a widow. And there were many lepers in Israel in the time of the prophet Elisha, and none of them was cleansed, but only Naaman the Syrian.” When they heard these things, all in the synagogue were filled with wrath. - Luke 4:25-28
The same is reflected in the parable of the vineyard owner and the wicked tenants:
And he began to tell the people this parable: “A man planted a vineyard and let it out to tenants and went into another country for a long while. When the time came, he sent a servant to the tenants, so that they would give him some of the fruit of the vineyard. But the tenants beat him and sent him away empty-handed. And he sent another servant. But they also beat and treated him shamefully, and sent him away empty-handed. And he sent yet a third. This one also they wounded and cast out. Then the owner of the vineyard said, ‘What shall I do? I will send my beloved son; perhaps they will respect him.’ But when the tenants saw him, they said to themselves, ‘This is the heir. Let us kill him, so that the inheritance may be ours.’ And they threw him out of the vineyard and killed him. What then will the owner of the vineyard do to them? He will come and destroy those tenants and give the vineyard to others.” When they heard this, they said, “Surely not!” But he looked directly at them and said, “What then is this that is written: “‘The stone that the builders rejected has become the cornerstone’? Everyone who falls on that stone will be broken to pieces, and when it falls on anyone, it will crush him.” - Luke 20:9-18
In that parable Jesus is referring the Jews back to Isaiah and the Jews knew then that He was not only plainly claiming to be the Son of God and the rightful heir to God's Vineyard (Israel) but also indicting their stubborn unbelief and they were incensed:
Let me sing for my beloved my love song concerning his vineyard: My beloved had a vineyard on a very fertile hill. He dug it and cleared it of stones, and planted it with choice vines; he built a watchtower in the midst of it, and hewed out a wine vat in it; and he looked for it to yield grapes, but it yielded wild grapes. And now, O inhabitants of Jerusalem and men of Judah, judge between me and my vineyard. What more was there to do for my vineyard, that I have not done in it? When I looked for it to yield grapes, why did it yield wild grapes? And now I will tell you what I will do to my vineyard. I will remove its hedge, and it shall be devoured; I will break down its wall, and it shall be trampled down. I will make it a waste; it shall not be pruned or hoed, and briers and thorns shall grow up; I will also command the clouds that they rain no rain upon it. For the vineyard of the LORD of hosts is the house of Israel, and the men of Judah are his pleasant planting; and he looked for justice, but behold, bloodshed; for righteousness, but behold, an outcry! - Isaiah 5:1-7
Jesus was already concealed from the sight of Israel by the blindness of willful unbelief and no amount of word or deed can change that. They should have been looking for the Messiah that God had promised rather than inventing for themselves hope in a false Messiah that would rescue their nation from captivity, strengthen their political/religious power, and assuage their desire for self-righteousness. Those who had eyes to see, saw. Those who had ears to hear, heard. The rest were hardened.
God resists the proud and He will not be what we want Him to be: God IS. He has spoken to us in His Son and if we truly see Him we have seen the Father. What remains for each of us is to decide whether we really want to see Jesus as He is no matter the cost (to fall on that stone and be broken) or if we prefer to force Jesus to be what we desire. That stone will fall on us and grind us to powder. If we cry out to God with a pure heart He will reveal Jesus.
“Thus says the LORD who made the earth, the LORD who formed it to establish it—the LORD is his name: Call to me and I will answer you, and will tell you great and hidden things that you have not known. - Jeremiah 33:2-3