I'm not assuming they have to be small integers—I'm saying that
if the universe is built on discrete rather than continuous foundations, then small integers and coincidences at the bottom-turtle theory-of-everything become much less surprising. You're treating the space of possible charge values as if it's the reals, or at least some enormous range, but I consider that unlikely.
Consider: in every known case where we have found a deeper layer of explanation for a "coincidence" in physics, the explanation involved some symmetry or conservation law that constrained the values to a small discrete set. The quark model took seemingly arbitrary coincidences and revealed them as consequences of a restrictive structure. auntienomen's point about anomaly cancellation is also exactly this kind of thing. The smallness of the set in question isn't forced, but it is plausible.
But I actually think we're agreeing more than you realize. You're saying "this can't be a coincidence, there must be a deeper reason." I'm saying the deeper reason might bottom out at "the consistent discrete structures are sparse and this is one of them," which is a real explanation, but it might not have the form of yet another dynamical layer underneath.