I'll attempt a sensible comment on the subject of UFTs and symmetry.
The central theme in most unified field theories is spontaneous symmetry breaking. You try to model the laws of physics we see by guessing that perhaps the laws long ago were invariant under such-and-such a specific set of transformations, but that that symmetry was spontaneously broken in the very early universe, giving us what we have today.
Rather than being some vague undefined bunch of things, the symmetries in question are specific ways of mapping the fundamental fields to new fields in such a way that the mathematical form of the Lagrangian density (which encapsulates the equations of motion for the fields) is unchanged.
To emphasise: The symmetry transformations in question form a specific set with specific mathematical properties and relationships (they'd form a Lie group or Lie supergroup if you're curious). While the symmetry groups posited in unified field theories are indeed larger than the symmetries of the Standard Model used today, the rather vague claim earlier that "any possible set is a transformation" is definitely a false statement in such a context.
Invoking UFTs as support for doronshadmi's ideas makes about as much sense as far as decided to use even go want invoking set theory to do more look binary tree.