For many years after Jesus' death and resurrection, the only holy scriptures Christians had were the Hebrew scriptures (what came to be called 'The Old Testament'). Even once the apostles and others began to write about Christ and the growth of the new Christian Church, it took a while for enough copies to be hand-written to spread throughout all the expanding congregations of believers in Jesus. Those 27 documents were only completed around A.D.95 (with the last writing, Revelation).
That is the simple, and logical, reason why you do not read any command in what has come to be called 'The New Testament' to read the Old and New Testament scriptures every day. There might have been scope to instruct daily reading of the Old Testament for those who could get into a synagogue or the temple every day, for that was where the scrolls of parchment were kept. A very few rich individuals might have had private copies. Also, given that not everybody could read back then, a requirement for all Christian to do daily reading would be unreasonable. Think, too, of the many people whose eye-sight would be too poor to read - and no glasses were available then!
Even in the nation of Israel, before Christ, only a few would be able to read the Hebrew scriptures every day. The king was commanded to do that. But the two verses you cite speak about daily meditation of God's law. That does not actually require daily reading of the law. One can read, then meditate on the reading after they've put the scroll back and they go about their daily or weekly business. Even at night, king David spoke about not being able to sleep and meditating on that law, and he also sang psalms of praise (and composed them), with those psalms then being added to the scriptures later on. Again, the scrolls of scriptures were copied and held by well educated scribes. The custom was for people to gather and have someone read parts of them out aloud, publicly. They could not gather every day, especially not the majority who lived scattered throughout the countryside!
Yet the power and worth of those hand-written manuscripts was well known amongst God's people, and children were taught to read and to write, and to have scripture instruction in school. A huge emphasis was laid on children memorising great chunks of the scriptures - precisely because few would have access to written copies in later life. The modern mind, however, needs to adjust to the fact that books were not yet invented, and scrolls had to be kept safely in places like synagogues or the temple.
Once the last book of what later became known as The Bible was written, it is significant that it records Jesus as saying, "Blessed is he that keepeth the sayings of this prophecy of this book." It also speaks of hearing the words of that scroll:
"For I testify unto every man that heareth the words of the prophecy
of this book, If any man shall add unto these things, God shall add
unto him the plagues that are written in this book. And if any man
shall take away from the words of the book of this prophecy, God shall
take away his part out of the book of life, and out of the holy city,
and from the things which are written in this book." (Rev. 22:7 &
We know from what was written about Jesus that he taught followers how the Hebrew scriptures were fulfilled in him. Then, on the road to Emmaus, he said to the two believers,
"O fools, and slow of heart to believe all that the prophets have
spoken [in the O.T.]. Ought not Christ to have suffered these things,
and to enter into his glory." And beginning at Moses and all the
prophets, he expounded unto them in all the scriptures the things
concerning himself." Luke 24:25-27
You can be sure that those enlightened disciples would make every effort to then get reading the O.T. texts Jesus had explained to them. And when, years later, the N.T. accounts were written, they would be avidly read by all who could do that. They wouldn't be able to get enough of them! Nobody would need to command them to read every day! They would, if they could.
It is tragic that, today, when the scriptures are available in thousands of languages, in print and on-line, that there is an awful dearth of reading them. There probably is more ignorance of the scriptures now than at any other time after the Reformation. People are so easily distracted with what their eyes see and what their ears hear - they are so busy working, playing, going on holiday, shopping... a hundred and one excuses can be made. But those who love their Lord soak up the scriptures at every opportunity, not as a duty or obligation - but because they love the Lord, and the scriptures are all about their precious Lord.
Christians do not need to be told what they should do. They know what to do to please their Lord because they know his words and the value of the scriptures.