It’s always had that element for coaches and execs but since the 1990s it seems to have gotten real bad. And now with players and one years contracts, they’re all recycled mercenaries. Tough to build allegiances and follow player’s careers with a fans fave team. Nowadays, Warren Moon and Ron Lancaster would plays for 6 teams in 7 years, 2 being names Rough Riders/Roughriders. CFL would be wise to figure out how to retain personalities in same locations for extended durations to build fan interest.
I feel like in the past almost every team had "a guy" in the sense that it was someone that had been with the team for a while and anyone's Grandmother could recognize. Lots of teams had more than 1. Here's a few off the top of my head from around the 1995-2005 era. Probably even missing a few.
BC - Geroy Simon, Pasaglia
Edmonton - Ricky Ray, Gizmo, Pless, Hervey, etc, etc.
Calgary - Pitts
Saskatchewan - I'm actually struggling here haha. Probably an obvious one I'm not thinking of
Winnipeg - Stegall, Westwood
Toronto - Pinball
Hamilton - Montford, Flutie
Montreal - Calvillo
Now? Other than Winnipeg I don't know if a single other team has that "guy" that even people that don't watch or care know about.