migtig - For my part, I try not to conflate the service a bank provides me in handling my day-to-day finances / transactions (e.g. checking account services) with whatever return it might give me on excess (i.e. not immediately needed) money that I might choose to deposit with / loan to / invest with it (e.g. in the form of a savings account or money market fund).
When it comes to the former, I very much prefer doing business with brick and mortar based banks. They offer a number of advantages, and at this point almost all of them offer online functionality as well. And, I don't necessarily expect them to pay me (e.g. in the form of interest) in connection with providing me those kinds of services. The value of those services over the course of a year (as well as the cost to them in providing them) is probably greater than the value represented by their getting to hold (i.e. otherwise use) a couple thousand dollars for a year.
So I like to keep a minimal amount of money in an operational account, an account that I use for day-to-day or month-to-month stuff. And I'm happy with them just servicing that account for free, that seems like a pretty good deal to me. Money that I don't need in the short term, even that portion which I don't feel comfortable investing in some way (e.g. in equities), is deposited in some other account / form. With regard to that money I'm then free to seek the best combination of return / safety / liquidity suitable for it - that could mean using an online only bank, a different brick and mortar bank, or the same brick and mortar bank; and it could mean any of various kinds of deposit accounts or other instruments. That also leaves me free to seek the best fit for the operational account based on the criteria that matters most if it - e.g., location convenience, policies / fees, friendliness (read: cuteness?
) of staff; not so much the interest I get on that money as that's less important for that relatively small average balance.
Anyway... sometimes we try to combine functions and doing so yields significant efficiencies. Other times we try to combine functions and it yields a worse result with regard to the respective functions. I think this is an area where the latter tends to be more true. Saving money is different than having money immediately available to deal with normal expenses. What matters most regarding the former can be quite different than what matters most regarding the latter, so I think we more often than not do better to think of them separately and make decisions accordingly. The point being, I myself probably wouldn't use an online checking account (meaning one with a bank that didn't have local brick and mortar locations). But, because I'd want my checking and savings accounts separate anyway, I might consider one if the interest they offered was meaningfully better than I could get elsewhere and their policies met my needs.
