I don't think what's keeping "ordinary men and women" from becoming politicians is the toxicity public figures are exposed to, considering a lot of "ordinary men and women" (but particularly women, gender-non-conforming men and PoC, especially if they're trans) get the same or worse on a daily basis on social media.

If you look at the careers and upbringing of most high-ranking politicians, I doubt the most obvious distinction to common folk would be particular thick skin -- heck, the sitting POTUS isn't exactly thick skinned and that's arguably the most publicly exposed office in the world.

Hint: it's wealth. The distinction is coming from wealth and having connections with wealthy people who supply you with funding and influence.