Yes, it is true that quantum mechanics breaks apart at large scales (and something that loop quantum gravity and string theory try to amend), but isn't this what would make quantum mechanics a partial theory, as a minimum?
On the other hand, it is quite widely accepted that the universe is finite and roughly 92 billion light years in diameter and that time is also finite and about 13.8 billion years, so none of these are infinite by any means (large, yes, but certainly not infinite). It is also accepted that our universe started small and expanded at an accelerated rate (evidenced today through red shift in the Cosmic Microwave Background radiation, etc.), so the degrees of freedom closer to the initial state must have been smaller than today, right?
A more general question that could be posed is: even though we can experimentally test many predictions that quantum mechanics makes (in a similar way that we can experimentally test predictions of Newton's laws of motion), are we getting to a point where we are facing the limitations of this body of knowledge but, because we have no better option, we are coming up with either non-falsifiable (please no flame wars here) theories such as M-theory and string theory, or just plainly ignoring the elephant in the room? Are there new and upcoming theories that are both, falsifiable and plausibly true, even if not complete and/or verifiable today?
Last but not least, are we closer to a point where we should start considering abandoning unitarity as a requirement for quantum operators? In quantum computing, unitarity is quite nice since it gives you full reversibility, no information loss, etc., but is this how the universe operates at large scale? It is true that quantum computers have a fixed number of qubits and this really doesn't matter (your vector's size never changes because qubits don't magically appear out of thin air), but expansion in the spacetime continuum does seem to appear out of thin vacuum. Is the universally accepted Schrodinger equation missing a term or two?