Only Saving Throws?

I’m mostly curious about if this mechanic is used in any existing ttrpgs or how well it might work as a mechanic. I’m wondering about a system that only has saving throws (fortitude, will, reflex), where you only roll to avoid dangers and their consequences. There are no ability checks made to lift something heavy or balance on a ledge or investigate tracks. How well would a system like this work? Is it to barebones? Could these saves be used to avoid attacks or would an auto hit system work better?