The way I see it, TPA have two potential advantages for a company.
1) It's a marketing expense, Which helps you come tax time, the more you spend building your business the less tax you pay.
2) If you have a service model business with clients for example, you could have a client day at your company where they can come by, have a drink & a feed, and meet a fair dinkum NRL player. Clients lap that stuff up, it makes them really happy and goes a long way towards keeping that client, and possibly expanding what they buy from you. Depending on what business you're in, that could be worth a lot of money. Think of it this way, lets say you charge $10K for X service, You have a client that happens to be a mad parra fan, he already takes X service, but you see an opportunity to sell him Y service as well, for $50K. You have a TPA agreement with Normy for $25K, you get him to come out to your office or wherever to meet your client (and some others as well), of course the client is gonna show, he wants to meet Normy. While you have him there, you sell him on Y service, and he's so chuffed to meet Normy that it helps get the sale over the line. You've now increased your revenue from that client by $50K.
That's the advantage that TPAs have for businesses. There's also a philanthropic element as well, as MJC mentioned, they're more than likely fans of the team that want to help out.