Remember their origin story is that a bunch of brave revolutionaries who the British called traitors and criminals threw off the shackles of tyranny (a word that we tend not to respond to in the same way) to form a republic.
Part of the foundation of that was to remove the power of the state to oppress. Otherwise you could convict someone of any old trumped up charge and thus prevent them from running for office. Effectively replacing the overseas tyrant with a homegrown one.
TL;DR is the founding fathers did not want to exclude a felon from office. It's no accident. They didn't "forget". They didn't have a golf match and finish early. They thought about the possibility of a future government going rogue and tried to account for it.
That's my take on it having read more than I care to in helping a family member get their citizenship. And that is how they see it.