I've read this sentiment before, but could never understand why. Is something about this question that is fundamentally different from normal questions in number theory?
The Collatz map itself gives a discrete dynamical system, which we can't tackle in general. Conway showed that a generalization of Collatz, where 3 is generalized to any odd prime, is Turing-undecideable.
I'm not a number-theory expert, but I think that non-primitive-recursive functions (iteration/recursion that isn't bounded ahead of time) don't really show up in number theory at all.
Not that we know of, and yet the proof is still illusive despite many great minds attempting to solve it. That's what makes it so alluring.