OSR: Thoughts on Thieves

Something I've been pondering about OSR rules is why don't Theives have the best Saving Throws? 

Wouldn't that have been a good alternative to Thief Skills?

It's something I've been thinking about recently and in many ways I think Saves could be thought of as "skill checks", sure perhaps you won't die or be paralyzed or poisoned, but if there is no consequence to a "skill check", like a Save, then what was the point of it?

Any opinions would be appreciated.