Vault/Counting House I could see in an engine.
I did that once with Cache and Counting House.
I actually brought up Cache/Counting House here.
I mean Cache and Coppersmith, in addition to Vault and Counting House. I believe there were some Worker's Villages in there as well.
Then once is the operative word. You did it once. You're not reliably pulling off a massive draw engine with all your Coppers plus all the Treasure cards from the Cache(s) you bought. Not against a decent opponent, anyway.
Also - query: will the Base Cards set be updated to include Shelters and Ruins?
I would be a little surprised (and disappointed) if the Shelters and Ruins didn't already have art. My hope is that they either have text on them (and art on the top) or they have full-card art already.
I believe it was Worker's Village, Rabble, Vault, Cache, Coppersmith, and Counting House. Got a bunch of WV, few Rabbles, 1 or 2 Caches, couple Vaults, one more Counting House than Vaults, and a couple Coppersmiths. So i'd draw everything in hand, Vault it away, Counting House it back in hand, Vault it, CH, Coppersmith, buy everything. There was probably another Village in there somewhere.