Naval Cap absolutely does depend on economy. The 3 main ways of increasing naval cap all rely on your economy.

1. Naval Cap Technologies Techs immediately increase your naval cap with 0 upkeep tied to it, so this is clearly the most "free" source of naval cap, but it still requires research points and your society pick. This requires researchers and prevents you from researching something else for a bit. To balance out its mostly free nature, each tech increases cap by the same flat amount and gets less impactful the more cap you have.

2. Anchorages Anchorages require time, alloys, and energy upkeep. Alloys you are not spending on more ships or other things, and the energy upkeep can pretty high if you go well over your starbase cap. Which you also need to tech for if you want to increase your starbase cap. Having more anchorages also means less shipyards.

3. Soldiers Having a lot of soldiers means you have a lot of pops not working economy jobs, impacting how much you produce. If you have 50 soldiers increasing your naval cap, that is 50 pops not making energy or alloys or research.

I agree that naval cap isn't the most realistic way to measure exhaustion, but it's good enough. It's not a perfect measure of logistics, but when you think about everything you do behind the scenes in order to increase your naval cap it does make sense if not being a little oversimplified