That a non periodic signal eg something which is nonzero only in a short span, requires a infinite number of periodic functions i.e fourier series/transform to

That a non periodic signal eg something which is nonzero only in a short span, requires a infinite number of periodic functions i.e fourier series/transform to represent is better considered as a limitation of the basis, it simply cannot represent such, only approximate it by a signal with a infinite period, which is not the same as non-periodic to mathematicians. The definition of the signal implies its expression both in fourier and spatial basis exactly, with no uncertainty. For this to have an interpretation as uncertainty requires that the functions themselves have that interpretation.