> felons already can’t vote and participate in the electoral system
In some places, yes. This is already viewed as problematic disenfranchisement by many people.
> invoking the current age requirement of 35 to become president
In sortition, your ability to serve in office becomes your "vote". The age requirement of 35 in a sortition system disenfranchises younger voters in a massive way while in our current system it does not.
In sortition, selecting the "good ones" who are in the lottery is just a problematic as selecting the "good ones" who are allowed to vote in elections. While that doesn't mean we should have no restrictions, it does mean those restrictions should face very high levels of scrutiny and be treated as biased by default.
> it’s questionable that many would accept felons being “randomly” chosen to lead the country.
But again, sortition only works well if your sample is large enough to be reliably representative. It won't work well for selecting a president from a nation or selecting 2 senators from an entire state. This is because a sample of size 1 or 2 will always be prone to selecting outliers.
> who wins office by random chance did so by subverting the lottery
The integrity of the lottery, like the integrity of elections, is crucial to it's legitimacy. Our lack of experience with making this sort of selection process transparent, accountable, and hard to subvert is to me the biggest argument against sortition.