I do almost exactly what you described with Charles Schwab.
I have multiple "full" accounts, but there's no maintenence fees or anything. Their online tools are great. You can open a new checking account with the click of a button.
As I understand it, you need a brokerage account to get this; it's called the "High Yield Investor checking and savings account". It's not intended for most people, though apparently they don't care if you get the brokerage account and don't use it. On the other hand, Schwab has effectively zero physical branches, and apparently don't accept most ways of depositing money to your account, which makes it awkward to deal with cash and checks that end up in your hands for whatever reason.
All accurate. It is definitely marketed at investors, but I've used it as my checking account (er, accounts) for years now.
Although there are a handful of branches where I live, I never physically go there. I handle all check deposits via their mobile app. I never receive cash for anything though. You are correct, it would probably be a bad choice for someone dealing with a lot of cash.
And as a sibling comment said, no ATM fees anywhere in the world, ever.
I have multiple "full" accounts, but there's no maintenence fees or anything. Their online tools are great. You can open a new checking account with the click of a button.