Certain people here get pretty perturbed when a potential solution that wasn't asked about gets mentioned, but as a person who fishes from a solo canoe, I never can imagine why someone fishing "quiet water" would choose to use any kind of kayak instead. The only reason I can think of is that with a solo canoe, you actually need to learn how to paddle reasonably well (and you need to enjoy paddling to make that happen) to avoid forever being stuck within the "high-frustration" portion of the learning curve when fishing, whereas anyone can make a rec kayak or basic SOT go where they want it to on quiet water without much practice.
The big advantage of a canoe is that if you can kneel, you are much higher so you can see better and cast with a greater variety of motions (including better options for snapping your lure back under overhanging branches and into other tight spots). Also, when kneeling you can twist your upper body to face a broader range of directions, and the range of directions you can comfortably point your fishing rod is in turn amplified that much more. Try sitting on a flat pillow on your living room floor with your legs straight out in front of you, fishing rod in hand, and see how big an arc is available for casting or fighting fish. Then get up on your knees and do the same thing. There's no comparison between the two methods. Even if you don't kneel, sitting on the seat of a canoe gets you well up off the water, and there's plenty of room to pivot your seating position to the right and left. In any kayak, all you can do is position yourself facing exactly toward the front.
Perhaps a minor issue for most people, but a big one if you like hard-to-get-to waters, is that canoes are lighter than kayaks (especially lighter than SOTs) and even not considering the weight difference they are MUCH easier to carry.
I wouldn't go to the trouble of explaining this, but canoes are definitely "forgotten boats" today, in spite of the fact that there're a greater variety of fine solo models available nowadays than there ever were back when canoes were still king.