What we are saying is that the theory does not require a universal common ancestor. However, since the evidence does point to a universal common ancestor then it is part of the theory.
Well, actually I don't agree. The
theory is the description (model) of how populations evolve. It demands nothing about what has or will happen. The facts at hand say that there was a LUCA but the
theory makes no comment on that. It just suggests
how changes will occur from a LUCA or from multiple ancestors separately arising.
The fact is the evolution of life on earth (not the model of how it happened) seems to have a very early LUCA.