Yup. Authoritarians often criminalize their opponents to prevent them from running, like Putin did to Navalny. Even if banning felons from office could have positive effects, it's also a dangerous flaw that bad actors in power could exploit to maintain their power.
As to the first part, yes. If the founders had blocked federal office due to a felony conviction, just imagine the clusterfuck. 200+ years of anyone and everyone trying to get a conviction, of any kind, on their opponents.
Same thing goes for the second part. It's a roundabout way to block federal representation of certain groups of people. This is why automatically being blocked to vote because of a conviction shouldn't be a thing. As you say that would (and does) lead to a clusterfuck.