[phoenixstrike]

Just plain wrong.

  The postulates of Quantum Mechanics dictate that physical objects must be fundamentally spread out in the form of wave functions.

Even a senior undergraduate knows that QM is not resolved with GR. To quote a QM postulate like this as an argument against point-like objects in reality reveals more about your level of education in physics than anything else.

  At a certain point of abstraction, theoretical physics almost never has any direct correlation with empirical reality.

  Solutions to simplistic kinds of mathematics come in the form of idealizations called "points". But physical reality is fundamentally spatial...

Just so wrong... Empirical reality, as you like to say, specifically in collider physics, tells us that fundamental particles are point-like as far down as we can see.

I don't claim to have all the answers, but you are just being obtuse and passing by with a layman's philosophy and masking your lack of knowledge with stiff sentences.

Just because you don't understand it doesn't mean it's not true.