Pretty sure the kayak capacity ratings don't include the hull weight itself, so there's that. But you raise some valid points here regarding what a small floating hunk of plastic can realistically support. I have a smaller yak and try and shave off every ounce of weight possible. I bring two, at the most three rods. A tiny soft-side cooler with a few drinks and snacks, making a late lunch stop after. Small tackle bag with 1-2 waterproof 3600 size boxes.
For me it becomes like a zen thing to have to work within a slimmed-down framework: fishing FW bass for example, I'll concentrate on only one or two techniques and try and convince myself I'm Don Iovino and can catch anything on one 6" worm.
Here's an interesting video
https://www.youtube.com/watch?v=SNHuCrnk8fg on the effects of overloading a kayak.
That said, you may have seen those floating CreekKoolers: a sealed plastic tub you can tow behind you and use for food, fish, whatever. Expensive for what it is, but might be good to float your catch!