In a classic, legs-inside kayak, you keep your balance in the fluid motion of the paddling. We've all seen video or images of the classic "kayak flip," where the kayaker's whole body goes under the kayak and comes up (hopefully) on the other side, back in balance. The simplicity of this fusion of craft and body is a main reason kayaks have been so popular for so long.
When you move to a SOT type of craft, you're involving more of your core to stay upright -- and with a foot-powered kayak, you're even further away from that natural center of balance. That's good for burning calories, of course, but represents a major difference in practical use than we might notice at first.
This comes into play with fishing, especially, as one of the best things about foot-powered kayaks is the fact that, without paddles, your hands are supposed to be free. But in practice, at least before you become an expert in using your kayak, you're going to end up holding on for dear life. Combine that with the need for a rudder -- since you can't adjust your trajectory by simply using the paddles -- and you've got one hand on the boat and one hand on the rudder much of the time.
Changes to the length, width and body shape of the kayak are a necessary change here, but this in turn changes the speed and maneuverability of your craft. And if you do tip over, it's a lot harder to get yourself upright and/or out of the water.