The g-factor - a way to obfuscate reality?

In previous blog posts I have put into question the notion that the electron can only have spin of magnitude plus/minus one half of the reduced Planck's constant. It seems more natural to assume that the electron can have instead any integral value of the reduced Planck's constant. Leaving side for the moment the question of the possibility of higher order spins and focusing entirely on the magnitude of the smallest possible spin, a highly legitimate question arises: Have not physicists been able to measure this magnitude accurately?

Indeed, I asked myself this question and looked up an article on the Bohr magneton which says:

In atomic physics, the Bohr magneton (symbol μ_B) is a physical constant and the natural unit for expressing the magnetic moment of an electron caused by either its orbital or spin angular momentum.

This ought to be clear enough, hence, if we only measure how the electron spin interacts with a magnetic field in the same way be measure other types of angular momenta then we ought to settle this matter. So I was wrong then? Well, there is a catch, further down in the article we read:

The spin angular momentum of an electron is 1/2ħ, but the intrinsic electron magnetic moment caused by its spin is also approximately one Bohr magneton since the electron spin g-factor, a factor relating spin angular momentum to corresponding magnetic moment of a particle, is approximately two

So the g-factor is approximately two, what a coincidence! Or was it rather put to two?