I'm not.
But for those who are, the best reason to be loyal would be that you know the manufacturers personally, or they've done something great for you or your local scene.
The best reason to be single brand would be to simplify your choices. Within one brand you can pretty well fill a bag, without having to test 10,000 different models/plastics/weights for the next magic disc that will make you a star. It won't be quite as fine-tuned as a mixed bag, but it'll do.
I agree with this. There are so many choices available, with new releases coming out seemingly all the time, even within a single brand. Sticking with something tried and true simplifies things. Plus, you actually get to learn the discs well and gain a lot of familiarity compared to chasing some "magic" disc that will change your game.
In the course of learning about the game, I've thrown and own various brands of discs but I have stuck with Innova discs for a few reasons:
1) I started out with them and have a predictable range of expectations from the core molds I throw. This also gives a good basis for comparison for other discs/new releases. In addition, I have gotten to a point where I have a good stash of backups and throwers in different stages of wear.
2) They work for me, and as I improve my game, I continue to find new ways to use them.
3) They are widely available at competitive prices. If I am traveling and have an opportunity to play but didn't bring any discs, I can easily go to a number of stores (in the US, at least) and get an Aviar, Roc/Roc3, and some sort of dependable driver like a Leopard/Teebird/Valkyrie/Thunderbird. Instant 3-5 disc bag that I am comfortable with playing at any course.