I don't have a yak either but I plan on getting one sometime this year. I've been wondering the same thing as you. It doesn't sound like too many people fish from kayaks but I don't see why you couldn't. It's a nice and affordable option for those of us who can't afford a boat just yet.
Actually there are tons of people fishing from yaks all over the country, especially along the coast(s). And from what I gather, it has nothing to do with affordability but more about being able to launch from just about anywhere (you don't need a ramp) and being able to get into areas that a boat just can't reach. Many kayak fishermen like Forrest have given up their power boats because they prefer fishin' from a yak. Many also prefer the quietness and the chance to get a little exercise while they are wetting a line.
Texas Kayak Fisherman is a very active website of local interest. There are a ton of others.