Having autosave on by default makes my storage insanely full with replays of others before I've even started one.

Yea u have this option in settings

This is new.

open game client, open settings by clicking the gear icon in the bottom right corner, go to the Game tab, find Autosave replays and switch it to 'Only save mine'

that's exactly what you're asking for and it's already part of the game