Houston really set the current model for tank/rebound, but it's worth noting they did it at a lowpoint and they did it at a cost, and other teams who have tried to follow that model have not been as successful, if you call the Astros one title, two pennants successful. Please keep in mind they tanked to get a top draft pick -- they did not sign! They missed on Kris Bryant. Now the Cubs made it popular for teams in big markets to think about how to tank/rebuild without the ZERO TV ratings but also without the planned success to rebuild an organization stronger and have the players and structure to nourish sustained contention.
(Sorry for the delay. I accidentally deleted my answer and had to recreate it.)
The Cardinals, internally, talk about trying to tank like it's a four-letter word. They don't think it's true to their brand. They don't think it's a model that the fans will like. They don't think they can sell tickets through it, and I bet neither do you. So they don't really follow that model, and the fence-sitting has been an issue, one that Mozeliak acknowledge as far back as 2015 was on the horizon and they had to figure out a way not to be stuck there. The Cardinals, in the industry, are seen as a model of consistency -- winning record, consistent revenue (relative do to pandemic), devoted fan base, and a continuity of leadership that is the envy of some owners. Check around some of the comments that managers and executives make about the Cardinals. A few pitchers at the All-Star Game told me that the Cardinals are always lurking and have a surge in them. Kris Bryant mentioned how the one constant during his time with the Cubs was that the Cardinals were always in the race until the end -- except for the one year the Cubs ran away with it. He said that as a compliment, not bragging. The Cardinals are viewed by agents as conservative and sometimes frustrating because they don't move off of their valuations too much, and that can also frustrate other teams, too, when they try to make a deal. The Cardinals are not viewed as a team that you trade with to "win" the trade. However, the Cardinals are benefitting from their reputation in the industry for developing and identifying players -- from Garcia to Arozarena, Gomber to Alcantara. Teams see those players succeeding elsewhere and wonder what the Cardinals are doing to acquire those players, identify them, even if they don't ultimately reach their best with the Cardinals, or even blossom with the Cardinals.