FPS Capping Question: Better Effects and/or Resolutions?

I have a specific thing I'm curious about re: capping FPS.

I understand that capped FPS will result in more consistent image overall (lower peaks, and thusly higher dips), less tearing, less power consumption & heat. I get all that.

What I am specifically wondering is whether setting a lower FPS will allow a card to apply better, more advanced effects, and even display higher resolutions.

In my mental model, the little gremlin that paints 80+ pictures every second in the computer's Gremlin Portraiture Unit can only apply so much detail, given all the pictures he needs to paint. So my assumption is, if you tell him he only needs to paint 60 or 72 paintings per second instead of 120 or 144, he can take his time and include more detail, better reflections of the happy little trees on the peaceful lake, or even more brushstrokes total.

Is this how this works? Would capping FPS at 60 create more graphical leeway to crank a game's settings up to ultra? I ask because as my eyes age, I am definitely experiencing diminished returns on FPS beyond 72, or even 60 fps. Which I am taking into consideration as I do my mental calculus around just how much card I would like to buy this summer.

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Thanks!