That doesn't matter. You could imagine a system that accumulates two terms: (actual result, junk). Instead of deleting something it just adds it to the junk part of the pair. Maybe the junk part itself has computation which never ends, but it doesn't matter because you just extract your result from the left part of the pair.

I don't follow your argument. Why must we have the ability to "delete" sub-expressions?

Consider a computational model that, rather than work by successively rewriting an expression over and over in a way that honors some equivalence relation over expressions, it works by explicitly building the sequence of such expressions. In that kind of system, every computational state properly contains the previous state. Things grow and grow and never get "deleted". Yet such a system can clearly be universal.

as far as I understand it, turing completeness is a weaker property than combinatorial completeness, which Craig's theorem is addressing. The nonexistence of a singleton combinatorial basis doesn't necessarily imply the nonexistence of a turing complete combinator.

An implicit K suffices for universality, as in \x\y\z. x z (y (\w.z))

Coincidental timing for Wolfram to pop up here just as it becomes clearer that he might actually have met Epstein after all.