Let’s be a little realistic. One becomes a felon by way of the justice system and is sanctioned through a proper legal system, though I am aware it has many shortcomings. Your examples are not analogous. People can lose a lot of rights when they are convicted of a felony and voting is one of them. I personally would prefer all rights be restored once someone has served their sentence but I can’t agree a felony conviction is comparable to poverty or a lack of an education. Unless you also want to set up a judicial system that decides on whether poor or uneducated people should be allowed to vote.
A person in a democracy who wants to govern should also consent to being governed. It’s considered a bad thing if politicians make themselves exempt from the laws they write, and the same problem occurs if a voter wants to enact new laws but refuses to abide by the law himself.