So if you have exactly N bad cards in your deck, then playing N Digging Vagrants will put them all in your hand. That seems like a good thing, as the value of all other drawing cards is increased. But you're probably not going to play all of them unless you also have other drawing, in which case you're as likely to draw the Diggers as you are to draw the junk they're supposed to be digging. And reshuffling issues. I guess if you were going to use them then you would want a lot of them, so maybe they need to be cheap.
It does have a lot of synergy (Forge, any trashers, Baron, Island, Ambassador, any discard-for-benefit card, Death Cart and Crossroads as mentioned before, etc.). I was thinking it would excel in this cases, but maybe not.
So maybe $2 does work. It would be interesting to see.