Those approaches aren't mutually exclusive. You can easily learn theorems and math concepts using Anki and then apply them in practice.

You can learn words in foreign language using SRS and then use those words in conversations, when reading, watching a movie, etc.

I don't see any value in the purist approach your propose.

Also:

> So when we use this sort of spaced repetition we're trying to artificially "warm up" the cache in our brains.

No idea what this means. It is no more artificial than actively seeking out people to talk to just because you want to learn a new language, or forcing yourself to prove theorems just to better remember a mathematical concept.