> Also trivially there must be some non-halting program with the highest number of steps.
That isn't trivial. Whether a given program halts might be independent of ZFC, or of any consistent logical system you might try to use. The question of whether such a program "really" halts is one which might not have an answer. ZFC claims there must be an answer, because LEM, but why should we care what ZFC or first order logic or anything has to say on the matter, if they can't actually tell us whether it halts?
Trivially a non-halting program for any n exists. Also trivially there must be some non-halting program with the highest number of steps.
We can’t necessarily find that program, but there is almost by definition some non halting program with the highest number of steps