Quantum field theory and relativity share the need for point particles (besides we have learned how to deal with extended objects with more or less success). Heisenberg uncertainty principle introduces a limit into the simultaneous measurement onto a point particle and generalizations can be found for p-branes in the literature. However, is it really unavoidable that point-like particles will loose their sense in a quantum theory of space-time, if this space-time is only effective, what are the pointless geometry we are seeking? Even string theory, as we understand it, makes use of the conformal fields, but can we avoid points (and space-time or fields at the end!)? If so, why are they so precise? Do we really have a way to probe if REAL point particles are meaningful or only a deep and useful model of reality?
"In quantum mechanics, the concept of a point particle is complicated by the Heisenberg uncertainty principle, because even an elementary particle, with no internal structure, occupies a nonzero volume." Wikipedia