The appeal is that it would make being a career politician impossibleThe assumption, and I'm not saying that it's necessarily wrong, is that "career politician" is undesirable. How about getting rid of "career software developers"? Get rid of those entrenched JavaScript devs that are only interested in feathering their own nests. "Career doctors"? The medical profession is really just a business, and it should be treated like one. Next time you break a limb, seek out an MBA instead.
Point is, the more I've been involved in politics (including running for office) the more I realize that you're not just going to march in on the first day and get stuff done. Kind of like that first day with that new codebase, eh? Now, I don't know that one out to be "Congress critter for life", but you don't just waltz in an go "my constituents want $THIS" and expect it to just happen. So a little experience might go further than electing the "outsider" who isn't "beholden to special interests".