To be clear, we say that an electron has -1e charge: that "e" is the absolute value of the charge of an electron. The charge of an electron is approximately −1.602176634×10^−19 Coulombs. Quarks have either +-2(1.602176634×10^−19)/3 or +-(1.602176634×10^−19)/3 coulombs charge.
It's a fraction because we simply decided it was easier to describe an electron's charge as "e" and quark charges as being a fraction of that. It's entirely by convention.
We could've just as easily have described, like you mentioned, a quark to have either +-q or +-2q charge and electrons have -3q (where q=(1.602176634×10^−19)/3 C). We just happened to find electrons significantly before. It's also convenient as we don't see free quarks so every charge we see in the universe is a multiple of e, there's no advantage to going smaller than that.
