To counterpoint the first end: teams like the Dodgers and the Astros do so because they're not attempting to win on the margins. The Dodgers can try an Andrew Heaney or an Alex Wood every year because even with those players, they're going to win 93-95 games. Come the playoff time, they bin these guys if they suck, or replace them mid-season with a purchase. Teams like the Rays do so out of pure necessity; they can't not try to fix people. The Cubs are in a goldlilocks zone right now of not being good enough to throw innings or PA's away while not being so incapable of spending that they have an excuse not to find better. If the Cubs were a hands down 90+ win team, I'd be far more amenable to the Cubs playing and tinkering with guys who offer useful profiles if they can work magic. Currently, the Cubs look like they'll probably enter next season in that 85-88 win territory. Good enough to be paper divisional champions, but not so good they have innings to just throw away.
While I think a trade could change the equation, I'm not sure they're going to ever to a stage where it's so drastic they have innings for Turnbull. Currently, the Cubs have: Steele, Hendricks, Taillon, Wicks, Smyly, Asad and Wesneski who are likely to make starts in 2024. They'll likely add at least one SP, and maybe two raising that number to 8 or 9. It's a forgone conclusion barring injury that Cade Horton will likely vault into that group by June. Even with a trade where the Cubs lose two of those, Spencer Turnbull is, what, 8th or 9th in line? For someone who wants to resurrect his career, that's not good odds when someone like, Oakland will probably put you 6th in line or so. For the Cubs, you still remain in a situation where you're so very unlikely to use him.
Another year, another Cubs team and I think Spencer Turnbull, as explained by yourself, offers an interesting amount of data that suggests with work, tweaks, and changes (don't want to discount that. This is good stuff, Matt!), there's a useful MLB arm. I just think the Cubs aren't either bad or good enough for this to be the best place for him to do that. So really all I disagree with is the "Cub" part.