Not for naught! I think I see it more clearly now. Form a theoretical point of view, there is no limitation in having perfectly sharp position states. But in practice that implies an infinite energy.
What about the creation of a particle anti-particle pair when you try to do that...
What are the theoretical and practical reasons that no particle can have an absolute sharp position?
Is it because the position operator has no eigenvectors, i.e. position eigenstates are never descriptions of actual physical states (because they are Gaussian vectors with a certain width)...