Jesus is said to have said, "Will the Son of Man find faith left on the earth when he returns?" In context this looks like a rhetorical question, with the answer being "no", at least more or less, even if he did not mean that no one at all would believe. So I don't see how your second thing is right, since someone seems to have predicted that scenario. It's true that that is likely to happen if Christianity is false; but apparently it is also likely to happen if it is true.

First, I don't think it's at all clear from the context that the answer is intended to be "no." Second, Jesus also indicated that some people who knew him in person would still be alive as of the time he returned to earth, so this might be better interpreted as skepticism that his followers can maintain their standards of devotion rather than doubt in the persistence of a long term tradition.

As for better documentation, Thomas Aquinas at least asserts that the reason faith should work miracles is that a person who has faith "merits" in a certain way to prove that faith to himself and others. This means that equal faith should earn equal proofs. But an equal miracle will be more capable of proving things, not equally capable, when you have better documentation; so as documentation improves, the faith you need to work the same miracle will increase, and so the frequency of miracles of a given type will decrease. This also explains why most miracles are not directly visible in a moment; because a miracle like this has too much of a capacity to prove something, in comparison to people's level of faith.

On the other hand, Jesus himself seems to suggest a simpler model in Luke 11, according to which God answers prayers simply to satisfy those who ask, because he is good.

If unbelief inhibits miracles, then one should be able to create miracles by separating out enclaves of the faithful (and indeed, more religious communities certainly tend to segregate themselves from less religious ones.) But if you go too far down the road of expecting no miracles to occur, then this also means that you can't update your confidence upwards based on reports of miracles either.