So I think this is partially true, but it can be a bit more cloudy.
We would argue Wisconsin has generally maintained the same identity since the 90s, with maybe a three-game detour when Anderson tried to spice in a little spread stuff. But that identity has oft seen subtle shifts in the plays/concepts. In 2010, UW was a inside zone/power/pin-and-pull team. Now they run power in a way that looks like counter, lots more counter. When they had Jonathan Taylor, they worked in more outside zone, something they used int he 90s but rarely under Chryst.
Sometimes I think identity is as much a spirit as anything else. A style you build to. The Leach Air Raid is a rather rigid on, but some are not. (It also helps when you're either good or at least seem like you have an aim. Kentucky is worse than Michigan, but you knew their identity. I think some years, Michigan has trended toward and identity, just not one that people wanted when it wasn't effective. A lot of the best offenses get their identity because they're just crushing folks, so we see their distilled from)
You can massage the system to your talent. Wisconsin is different when they have a good QB. It doesn't mean they go air raid, but they're more capable and willing to open it up. When you have an RB that is more suited between the tackles, you don't run him on a bunch of sweeps. When you have an RB that is better in space, you make use of that instead.
Sometimes it might be as simple as bringing in a new OC or a new OL coach that wants to teach certain concepts in different ways than the predecessors, or has different ideas about what does and doesn't work. As long as they have the right talent for what they're trying to do, changing identity in that way doesn't mean you don't have an identity.
Jeff Brohm is an example of someone who is struggling between what he wants and what his players can execute. He wanted Sindelar to be his QB. Big guy, strong arm, can rifle it 40 yards downfield on a string. But you can't throw 40 yards downfield when you don't have great WRs to get open and don't have the OL to keep your QB vertical, so he kept going back to Blough. Blough didn't have the arm, but he could evade the rush and extend the play. Now we're getting the WR talent and the OL is improving [but still below average], but now he's having trouble getting the QB who can make the throws that he wants.
Now, part of it might be just a lack of talent. But these guys are all FBS athletes, and increasingly as he gets more good recruits, these are guys who had better-than-MAC offers. He's just having trouble trying to figure out what identity fits his players, instead of trying to get players shoehorned into his preferred identity.
