In high-quality Treasure decks, Bank is ordinarily not that useful, since you don’t have enough Golds and Platinums to make Bank worth very much. But Venture, which does best in high-quality Treasure decks, provides Bank with the quantity it needs to improve its value. If you have Bank and Venture in hand, each Venture is worth at least $2 + ($1 + value of card drawn), as opposed to Gold, which is capped at $4 with the Bank. So even if the Venture hits a Copper, Bank + Venture is always equivalent to or better than Bank + Gold, and is much more affordable.
Better yet, if you have a sufficient concentration of Ventures in your deck, Ventures can often draw three or four Treasures. With Bank in hand, each Venture is worth $2 + at least $2 per drawn Treasure with the Bank; a Venture that hits another Venture is therefore just as valuable with the Bank as a Platinum.
Adventurer can be substituted for the Venture, but it doesn’t work quite as well. Although it always draws two Treasures, it isn’t a Treasure itself, so it only does better than Venture if Venture doesn’t chain into other Ventures. In addition to not chaining, Adventurer also costs an Action to play (which incidentally means you can’t play it on the Black Market) and it costs $6 (which is both harder to get to and in direct competition with Gold). Adventurer does have one other advantage over Venture: instead of playing the Treasures, it places them into your hand. This can be helpful if you are looking to avoid playing Loan or Venture, or if you have Mine or Mint.
Counting House instead of Venture works on a similar principle, though Counting House is a strategy all to itself. It’s more risky, since it depends on when it’s drawn, and it only gets you Coppers. But it is certainly capable of drawing in more Treasures than Venture or Adventurer.
This is an example of a game where Venture / Bank produces massive amounts of money even when the only way to trash Coppers is if your opponent Swindles them into Curses. It also highlights the weakness of Adventurer relative to Venture for the purposes of Bank.