If you had a point mass of amplitude, an infinitely sharp spike in the quantum arena, the amplitude distribution would not be twice differentiable and the future evolution of the system would be undefined. The known laws of physics would crumple up like tinfoil. Individual configurations don't have quantum dynamics; amplitude distributions do.

A point mass of amplitude, concentrated into a single exact position in configuration space, does not correspond to a precisely known state of the universe. It is physical nonsense.

It might be helpful here to remind the readers that one can concentrate arbitrarily tightly along some dimensions of the configuration space - for example, the position dimensions. In this case the state becomes wide enough in the momentum dimensions to maintain phase space volume. Physicist use this notion to an extreme degree all the time - Dirac delta functions, which concentrate all the way in one measure and spread out all the way in another, are ubiquitous when integrating.

And I wouldn't call considering the single-pointedness of the state in Hilbert Space a mere convenience of visualization. Multiple representations aren't just there for convenience - the set of perfect representations is an important property of a model.