This is a very late response, I know. But this is the thread that tops a Google search on this, so it seems the place to add an alternative suggestion to dealing with this that some might find useful.
You could write your code using SDL_WaitEvent, so that, when your application is not actively animating anything, it'll block and hand the CPU back to the OS.
But then you can send a user-defined message to the queue, from another thread (e.g. the game logic thread), to wake up the main rendering thread with that message. And then it goes through the loop to render a frame, swap and returns back to SDL_WaitEvent again. Where another of these user-defined messages can be waiting to be picked up, to tell it to loop once more.
This sort of structure might be good for an application (or game) where there's a "burst" of animation, but otherwise it's best for it to block and go idle (and save battery on laptops).
For example, a GUI where it animates when you open or close or move windows or hover over buttons, but it's otherwise static content most of the time.
(Or, for a game, though it's animating all the time in-game, it might not need to do that for the pause screen or the game menus. So, you could send the "SDL_ANIMATEEVENT" user-defined message during gameplay, but then, in the game menus and pause screen, just wait for mouse / keyboard events and actually allow the CPU to idle and cool down.)
Indeed, you could have self-triggering animation events. In that the rendering thread is woken up by a "SDL_ANIMATEEVENT" and then one more frame of animation is done. But because the animation is not complete, the rendering thread itself posts a "SDL_ANIMATEEVENT" to its own queue, that'll trigger it to wake up again, when it reaches SDL_WaitEvent.
And another idea there is that SDL events can carry data too. So you could supply, say, an animation ID in "data1" and a "current frame" counter in "data2" with the event. So that when the thread picks up the "SDL_ANIMATEEVENT", the event itself tells it which animation to do and what frame we're currently on.
This is a "best of both worlds" solution, I feel. It can behave like SDL_WaitEvent or SDL_PollEvent at the application's discretion by just sending messages to itself.
For a game, this might not be worth it, as you're updating frames constantly, so there's no big advantage to this and maybe it's not worth bothering with (though even games could benefit from going to 0% CPU usage in the pause screen or in-game menus, to let the CPU cool down and use less laptop battery).
But for something like a GUI - which has more "burst-y" animation - then a mouse event can trigger an animation (e.g. opening a new window, which zooms or slides into view) that sends "SDL_ANIMATEEVENT" back to the queue. And it keeps doing that until the animation is complete, then falls back to normal SDL_WaitEvent behaviour again.
It's an idea that might fit what some people need, so I thought I'd float it here for general consumption.