Strategy at Sports League Good Place to Start Career?

Off the top of my head I can think of two downsides:

1. Sports teams and leagues don't typically pay that well since they know they can lowball you assuming you're passionate about the organization (Disney actually tried to do the same thing when I was chatting with a recruiter trying to fill a role on one of their strategy teams)
2. I'd take a good look at LinkedIn to see what exits look like -- my intuition is that it won't be a very clear 1:1 path to a lot of the roles consultants typically try and exit to. Not only is it a fairly niche area, but strategy teams in general don't teach the strategy toolkit as well as consulting does

So if you're comparing vs e.g. MBB or T2 consulting and measuring from a perspective of increasing your earning and earning potential as quickly as possible I don't think I'd take it, but you're actually super into sports then I think the passion could make up for those downsides. Early in your career you can afford to take risks and try something out -- plenty of folks get to mid/late career only to wish they tried something they were more personally interested in. Worst case scenario you can probably do an MBA in a few years if you feel you need a reset and want to get back onto the consulting path