The Pauli principle was introduced as an ad hoc remedy to explain some features of many-electron spectra. Within the framework of non-relativistic quantum mechanics, it is introduced without foundation as an additional assumption, which has been shown by experiment to apply to all particles with half-integer spin.
Kaplan IG. The Pauli exclusion principle. Can it be proved?. Foundations of Physics. 2013 Oct;43(10):1233-51.
presents "heuristic arguments" suggesting " that the existence
in nature only the one-dimensional permutation representations (symmetric and antisymmetric) are not accidental." The physics behind the argument is that, if particles are indistinguishable, average values of one-body operators in many-body states must be independent of the state-labelling. The mathematics of the argument are found in
Kaplan IG. The exclusion principle and indistinguishability of identical particles in quantum mechanics. Soviet Physics Uspekhi. 1975 Dec 31;18(12):988.
Thus, there is some heuristic evidence that there can only be two types of statistics - bosonic and fermionic - because there are only two one-dimensional representation of the permutation group $S_n$ of $n$ particles.
There is no suggestion in Kaplan's argument that this is in any way tied to the spin of the particle, i.e. there is nothing to suggest that many-electrons states should be antisymmetric rather than symmetric, or that many-body states of - say - indistinguishable protons need also be antisymmetric; only that the many-body states must be one or the other. In this sense, introducing the Pauli principles, which follows from the antisymmetry of many-electrons states, was just an expedient for solving a particular problem in atomic spectra.
Moreover, the argument is completely rooted in the representation theory of the permutation group and cannot accommodate anyonic statistics (which can occur in 2d as quasiparticles, and where the permutation group is replaced by a braid group).
It is only within quantum field theory that the possible symmetry properties of many particle states were definitely linked to the spin of particles.