Pretty much all exchanges won't require you to have a USD Bank account, and it's just that you will withdraw your profits in BTC instead of USD. I doubt you'll find an exchange that could give USD without a bank account, that's just not right. Check https://coinmarketcap.com/rankings/exchanges/ for the rankings with adjusted volume. Choose any of the ones there and probably use BTC as a deposit and withdrawal.

FYI, you already answered your question. Just use crypto and you don't need a bank account. What's the point?