Well, first of all it's safer to have your game at FGL (if you use their Kidisoft free encryption service) than hosting the game yourself.
Second: Auction system. If you tell the sponsor "Sorry, but if you want this game you will need to raise your offer, because someone else is offering more than you"... He might think you are bluffing. At FGL the sponsor knows when he has been outbidded, and he can even read the terms of all the other bids. That makes it faster and easier to start a bid war. I have seen medium-quality games sold for more than $5,000 just because it got 2 stubborn bidders, and good quality games sold for $40,000 or more.
Third: Reaching the right sponsor. Big sponsors get a lot of mails from developers, sometimes they read them, sometimes they don't, but when they are looking for a game they use FGL search engine, or read FGL custom recomendation mails. They might be looking for a certain genre, or a high-quality game, or just browse the game lists. If you send mails, there's a good chance that your game will be buried or lost in the spam folder. At FGL if your game is good it will be highlighted, and those big sponsors will know your game is there, and I mean ALL the big sponsors, because all of them have an account at FGL, and they use it frequently. You know there who has played your game and for how long.
I can find many other reasons, but I'm not a fanboy... I know FGL has a lot of flaws, and that it won't work for many developers, but I have made 2.5x more money using FGL than outside. For "Days of Monsters" we tried to find a sponsor by ourselfs, because we had contact with some big sponsors. We got a good offer, but my partner wanted to try the auction, and at the end we got 4x more money.
However, if you start an auction, that doesn't mean that you can't email sponsors, but you will have to pay 10% anyway.