Electromagnetic charges are obviously quantized - I suppose the lowest charge being the $d$ charge of $e/3$. Every other charged particle has a multiple of that charge (actually all stable free particles have charges multiple of just $e$). The same is true for the $U(1)$ hypercharge charges in the unbroken electroweak theory. I'm wondering if there's a better reason for this than I was previously aware of.
I'm aware of Dirac's argument that if a single magnetic monopole existed in our universe, all charge would need to be quantized, or some quantum mechanical calculation wouldn't provide a sensible answer.
I'm also aware that there are unification theories, where the $U(1)$ hypercharge symmetry arises after the breaking of a larger symmetry group at higher energies, and the relative charges of the $U(1)$ symmetry in the low energy theory become integer multiples of each other.
Is there a better reason for charge quantization? Both of these reasons seem kind of tenuous. If you just introduce a fundamental $U(1)$ symmetry in a QFT, then it looks like you should be free to choose any coupling constant for each particle, so they wouldn't need to be rational multiples of each other. Is there something mathematically wrong with fundamental $U(1)$ symmetries of nature? Or is there some contradiction that arises when calculating scattering cross sections with irrational $U(1)$ charges? Or do you need to go all the way to Dirac's, rather convoluted, argument (assuming a particle exists that doesn't) in order to see the problem with irrational charges.
Basically I'm trying to understand whether or not the rational hypercharge values are proof of some kind of unification at higher energies. Or do all $U(1)$'s in QFTs need to have rational charges anyway, so it isn't proof of anything.
