Funny you should say this, because one of my favorite moves, and one I’ve been fairly successful with, is to deliberately pursue somewhat poor logic. It’s dangerous, regardless of my alignment, but it’s one of the best ways to get a lot of information. The thing is, if one pursues only solid logic, there’s no differentiation between how town and scum will react to it. The town will see the obvious logic, asign the appropriate alignment, and vote accordingly; the scum will see the obvious logic, perhaps with a bit of confirmation bias, and realize they have to agree with it. Sometimes even obvious logic will have a little bit of dissension, but that doesn’t really tell you much because there’s always that one guy who disagrees.
Instead, having somewhat spurious logic forces people to take sides in the discussion. Hell, I’ve taken straight up bad logic and pursued it for days, as both town and scum. As town, I got great reads on both the person I was pursuing and any other people who really decided to take part in the discussion. It will often get me under a lot of suspicion, for very much the reasons you outline, but that’s as much a blessing as it is a curse because I can then see how people pursue me and, of course, people under suspicion are less likely to be targetted by scum. One game, in fact, I deliberately played that way because I had a power role, so I figured it would be a great way to avoid night kills and give me a few days to use my power before I’d have to claim to prevent a lynch.
I’ve also pursued bad logic deliberately as scum, because it can be a great way to distract from meaningful conversation. If pursued properly, one can even drive a townie lynch that way, then fall back on the idea that one was just an overly aggressive townie. I don’t think I’ve ever quite successfully pulled that off, at least to the point of actual victory, but I’ve gotten really close with it a couple of times.