They're very stable, just so long as you stay seated. I've done it for many years and I've never tipped out unintentionally. I have taken a few intentional dips on hot days, mainly to assure myself that I can climb back onboard should I find myself in that situation in an emergency.
They can get a bit unconfortable if you're in them for long periods. My back starts to play up and my bum goes numb after a while. I usually just beach the yak and wander around for a while, then I'm as right as rain.
The thing I like about yaks is that I can launch anywhere. I like the fact that I can chuck it on the roof and travel lightly without the hassle of towing. I also like the fact that I can fish very quietly without scaring skittish bream. The Hobie is great for lure fishing, as the fact that it has peddles, means that you can fish constantly.
Most estuaries are fairly protected and it's usually quite safe to take kayaks into these places, so it's not very dangerous at all. My biggest fear is that I will get run over by some hoon jet skier when I'm at places where they're common.
If you've ever thought about using a yak. I can highly recommend it.