Angling kayaks are a lot more stable than they look, and you get used to the motion quickly. I can stand on mine (I have a Wilderness Systems Tarpon 120), but it's a little awkward to fish that way, so I don't bother since I typically don't have any need to. I don't use spooks much, but I've never had problems with hooksets on jigs, t-rigs, whatever while sitting. And I've never flipped except on purpose.
I can get places in a kayak I could never go on foot, and I can get to hidden, underfished backwaters through narrow/shallow channels that no bass boat can go. I can launch anywhere I can carry down or cart from my car. I can float smallmouth and trout streams too shallow for anything with a motor, and I can maneuver much better than in a canoe or jon boat or rowboat. And, of course, I can just go kayaking too if I want, without the fishing. What I can't do is carry every lure and rod I own, or cover a lot of water on a big lake. I tend to stay off really big water (I live 40 min. from Lake Michigan) because i'm not well-equipped for it, and I avoid busy recreational lakes because people on vacation and constant wakes are annoying (though not dangerous, really).
If a kayak will open up a lot of water for you, it can be a great investment...the only really "tough" part is figuring out how you're going to pimp it out...