TSN 1, 3, 4, and 5 generally show the same content at all times and each one is the designated "primary feed" for the different regions in the country. TSN2 is the only channel that consistently has different content than the other 4.
- TSN1: Primary feed for British Columbia, Alberta, and Yukon
- TSN3: Primary feed for Saskatchewan, Manitoba, Nunavut, Northwest Territories, and parts of Northern Ontario
- TSN4: Primary feed for Ontario, excluding Ottawa
- TSN5: Primary feed for Ottawa, parts of Southeastern Ontario, Quebéc, New Brunswick, Prince Edward Island, Nova Scotia, and Newfoundland and Labrador
Other than the regional NHL games, about the only time they ever have unique content on each channel is during big events that have multiple simultaneous feeds available, like the Tennis Grand Slams and the NCAA basketball tournament.
For hockey, Jets regional games air on TSN3, Leafs regional games air on TSN4, Sens regional games air on TSN5, and Habs regional games air on TSN2. During the games, that particular feed is blacked out for viewers outside their region. Currently, TSN1 is a "clean" feed without any regional commitments that require blackouts.
If TSN took on the regional rights to any of the 3 westernmost teams, it would mess up their distribution model and they'd have to black out the primary feed to some viewers in part of their region. I also don't think the Flames or Oilers would want to lose Saskatchewan as part of their region. So, if TSN took on the Flames, they'd have to come up with a system to black out the Flames regional games on the primary TSN1 feed in BC only and not black them out on the non-primary TSN1 feed in Saskatchewan only.