Or course, I don't mean to hand-wave away the potential implications of this. Maybe there would be no atomic nuclei in such a universe, for all I know. But if not, why not?
(The more interesting question would be the opposite: what if it was two electrons per proton? Then you could throw around some photons and end up with a half-proton negatively-ionized molecule. What would that look like?)
In reality, "protons" do not "exist" but are semi(very) stable collections of energy that interact in an interesting enough way in a group that it is useful for us to retain the name, rather than refer to it by its constituents.
Electrons don't really glob up into things like atoms due to repulsion (no moderation by the stron/weak nuclear forces) so we don't have a really useful reason to keep going beyond the definition of the electron so we just stop trying to find additional constituent parts.
Personally, I find the taste of hot chocolate just as nice regardless of the exact mix of quarks composing its constituent elements.
Not that it wouldn't necessarily be possible, but it would require everything we know about physics to be remodeled because the consequences are vast, fundamental even. So yes, with an entirely different model of the universe that would likely be possible.