Re the title, how sports franchises use IP, I haven’t read anything focused on just that though I should seek that material out. My belief gained through osmosis is that big sports (which in addition to pro sports franchises includes many collegiate and Olympic sports) heavily exploit copyright and trademark to extract revenue from and control broadcast and merchandise. Broadcast revenue is basically why big sports are huge as opposed to merely big.
Re how big sports affect communities/economics/jobs, a ton has been written, largely in the context of evaluating direct public subsidy eg for stadiums. As above, IP is also a huge public subsidy, as far as I know never evaluated. Anyway the studies regarding whether the subsidies are worth it in terms of jobs created or other community impact almost universally say no. I’ve occasionally linked to these on my personal blog, including most recent post. https://en.wikipedia.org/wiki/Stadium_subsidy is a decent summary but a bad article (needs references). The one reference it has http://econjwatch.org/articles/do-economists-reach-a-conclusion-on-subsidies-for-sports-franchises-stadiums-and-mega-events looks like a decent survey article, from 2008, but I really doubt there is anything new to say on the topic, other than citing newer and even bigger examples (Olympics and World Cup providing some).
There is probably also less econ and more culture studies literature on big sports impact which I haven’t explored and would also love pointers to. Dodger stadium is the classic un-subtle case, see https://en.wikipedia.org/wiki/Battle_of_Chavez_Ravine and of course countless media on star lottery system impact on exploitation of athletes and their families have been created. I suspect there are many more subtle impacts on broader communities that are under-documented, in part because they involve opportunity cost: what could have been if politicians and communities had more confidence in locally generated growth and thus less need to sell cheap to what Jane Jacobs called catastrophic money (probably obvious but I see the notion that big budget knowledge production is a must and therefore we need monopolies as directly analogous in knowledge space). Two other older personal blog posts are somewhat relevant, see Counterfeiting against inequality and addiction and Things that bring all the classes and cultures in a community together.
Going back to first paragraph, I suspect that without IP organized sports would be merely big rather than huge and catastrophic, and like games, more focused on fun rather than an arms race (broadcast and pay-per-view deals being the first order arms race for sports).