I wholeheartedly agree with @Anne talking about perceived im/balances and emphases placed on various types of gifts.
I wanted to add a bit of discourse on the Corinthians passages which you brought up and flesh out some of the themes a bit more.
I think @Anne is right in pointing out that while Paul is affirming the value of gifts such as prophecy and tongues, he is very much warning them against going overboard. Similar tendencies in the modern church provoke cessationalism. This tendency of certain modern churches (especially, but by no means exclusively, pentecostalism) to promote spiritual gifts leaves a bad taste in the mouths of many.
I will also define for the purposes of this discussion (noting that these aren't real terms, I just made them up) "strong cessationalism" as the view that these gifts have stopped and "weak cessationalism" as the view that people overemphasise or misunderstand the role of gifts in Christian life.
Disclaimer: I would consider myself a weak cessationalist.
The question seems to mostly address prophecy and tongues, so I will only talk about these for now.
Tongues
There is robust debate about what speaking in tongues even is. Classic modern tongues speaking is some form of Spirit inspired loss of personal control and "gibberish" (I don't say gibberish to demean but because I can't think of a better word) as an act of worship. I would very firmly suggest that this is not a biblical view of tongues speaking - one should look to Peter and the apostles in Acts 2 on the day of Pentecost as the model of tongues speaking. Here it is quite literally and very explicitly other languages interpretable by speakers of those languages even though the speaker does not understand. This is why Paul specifies that there must be an interpreter in 1 Cor 14:5 and why he says "various kind of tongues" in 1 Cor 12:28.
Moreover - how can you claim that a loss of control of your faculties is the work of the Spirit when Paul firmly asserts that the Spirit gives self-control (Gal 5:22-23). No, the Spirit gives us words, real words, to speak. When Jesus foretells the coming of the Spirit in John 14:15-16:15 he says that he will give us understanding of God's word (14:26), help us to testify about Jesus (15:26-27), convict us of sin and righteousness (16:8), guide us into truth (16:13), glorify Jesus not by worship but by the things listed above (16:14).
I have never witnessed someone accurately speaking a language they do not know, but I agree with the premise of the question that I see no biblical argument as to why this gift has ceased. I might tentatively suggest that we should consider something as 'mundane' as the delivery of a faithful sermon, tongues (as Peter gives in Acts 2), regardless of the language it is given in.
Prophecy
Regarding prophecy, it is also a matter of debate what it entails. No one can debate that at its core, prophecy is some sort of revelation or message from God. A narrow view would suggest that this must come directly from God, a more expansive view would suggest that it could come in the form of insight into the already written word of God.
This is the only gift I can think of where a robust argument can be made for a strong cessationalist view that it has stopped entirely. Hebrews 1:1-2 would suggest that there is no more prophecy because there is nothing more to reveal. I would tend to look at anyone claiming the gift of prophecy in the traditional, foretelling the future way with suspicion but not outright dismissal.
In my opinion, the only way you can say that prophecy exists today is if you take the more expansive view, including insight into the written word of God. Hebrews 1:1-2 precludes the idea that we can come up with new revelation of information never before revealed, but understanding of the words spoken to us only comes by the Spirit.
Conclusion
I agree that scripture doesn't point to an end date to the gifts given to people (asides from Christ's return). But this doesn't mean people practise gifts the way they were intended. The overemphasis and/or malpractise of gifts necessitates correction. I think strong cessationalists recognise this but overreact by saying that all gifts have stopped.
Regarding gifts, the overwhelming theme of New Testament is clearly that they should be used in love to build up and strengthen the church. This is clear from the passages you referenced. The public and sensationalised practice of gifts (particularly tongues, prophecy, and healing) is invariably aimed at glorifying the individual and not God. This is not how Paul said they were to be used. The testimony I have heard from people who have left churches that overemphasise gifts (but who are still very faithful Christians) is that they were made to feel lesser Christians because they, ostensibly, did not have certain gifts. This is quite the opposite of what gifts are for! see 1 Cor 12:29-30. So not only does the sensational practice of gifts glorify man and not God, it erodes the church rather than building it up.