A general manager has to be focused on many dimensions. One that I haven't seen mentioned lately is maintaining the revenue stream. How do you sell tickets (and the goodies like jerseys) after you wave the white flag? Maybe it's possible but you'd better have a damn solid and proven plan. And that goes for selling season tickets next off-season, if you leave a sour taste in the fan base's mouth in July this year. I think fans are much more forgiving (for a while anyway) of players who don't perform, than when the FO pisses them off.
Some will argue (and now I'm not particularly addressing you) that Twins attendance is already in the tank. I don't believe that is true. Year over year attendance seems to be up for the Twins. I scanned recent box scores for attendance and they've been playing to 25K+ houses, which even represents an uptrend. I believe instead they actually have quite a bit to lose if they are sloppy.
You could easily end up with an Oakland situation for the remainder of the season and on into the next. I think people totally underestimate what a chronic problem you give yourself once attendance dips below 10K a game. You don't just snap your fingers and get them back.
Looking only at the prospect haul one might get from Sonny Gray (as the best example) ignores at least 4 things, the other three of which have been addressed here and there in this thread: 1) the value that the player brings to the team's performance getting to the post-season, 2) the value of not entering the post-season with a crippled roster because you were pessimistic, 3) the value of a draft pick if they issue a QO and he rejects it, and 4) the fiscal disadvantage of tanking.