"sans-I/O" is one term for that style. I like it a lot but it's not a free lunch.

I always liked the phrase 'Hoist your I/O' [1] but yes, you can only hoist it up so many times until its outside of your application completely (making it completely pure, and now someone else's responsibility).

[1] https://www.youtube.com/watch?v=PBQN62oUnN8

Or "functional core, imperative shell".