If he polls well against Smith, for example, that would reveal a profound weakness in an appointed incumbent, and thereby encourage other entrants into the field. By contrast, if he runs for governor and gets crushed in the primary by Swanson, she’ll only be stronger as a general election candidate. Even if all Franken does is be a good soldier, raising money for Democrats and tweeting one-liners against Republicans, his party will have to reckon with his continued potency and what that means about how serious they are about zero tolerance — or, alternatively, if he gets little traction, Franken will have to acknowledge that he blew it, and his time has passed.
Regardless, his presence would force a public argument over his transgressions, and their political importance. That’s a debate worth having, and the political arena is the very best place to have it — because it is a political question.