For this to work, there have to be as many quarks in the proton as the denominator of the quark charge fraction. (And what mechanism forces that?)
And why should the charges on quarks be some nice low-number fraction of the charge on the electron? Why not sqrt(3) or something?
This is similar to how Ben Franklin, having no knowledge of elementary particles, defined the positive and negative polarity of electricity, so we have "electron holes" flowing from the positive end of a battery to the negative end in "conventional current." [2]
Edit to add: the electron's non-even charge numbers comes into light when you see that the charge is 1.602176634×10−19 Coulombs, where 1C/second= 1 ampere. If we were trying to come up with the definition of an ampere with nice base 10 numbers of electrons this would be much different.
[1] https://en.m.wikipedia.org/wiki/Oil_drop_experiment
[2] https://eng.libretexts.org/Bookshelves/Electrical_Engineerin...
Maybe they might have non integer charge.