I think there's also a (again silent) assumption that a constructor can be constructed, which is again non-trivial, and actually seems to be false. And if it is false then that seems like a major flaw, at least I don't really see how a non-constructable constructor is more convenient than the physical laws it is supposed to represent.

I also suspect you'll encounter something like the halting problem when trying to figure out which constructors aren't constructable. At worst you'll encounter constructors where this question is unanswerable (e.g. can you construct a constructor, which constructs all constructable constructors that can't construct themselves?).