Why should all species of elementary fermions have the same spin angular momentum?

Is there any deeper motivation behind the fact that all elementary fermions have the same exact amount of spin angular momentum ($frac{sqrt3}{2}hbar$ total or $frac12hbar$ projected) or is it really just an axiom of quantum theory? Because sometimes spin is described in terms of the transformation properties of the wave function under Lorentz transformations, and to me that alone does not imply the spin magnitude is actually the same for different particles. To what extent has it been experimentally verified that they are in fact all the same? In particular, if you measure the spin of a charged fermion, as in the Stern Gerlach experiment, doesn’t the deflection depend on the gyromagnetic ratio or whatever, in addition to angular momentum? In which case you’d be measuring something more like the ratio of the two, just like JJ Thomson could only measure the charge-to-mass ratio of the electron. Or is there a strong theoretical justification that they should all be equal?

And the same thing in regards to bosons.