Most established banks offer full online services. I see little advantage to an "online only" service when essentially the same services and rates can be had - online - from most brickandmortar establishments. There is no particular reason though that an online only service should be much different than a "real bank," if you're fairly certain you won't need to talk to them occasionally.
When I moved from WA state to KS, I left my principal accounts all with the credit union in Seattle, and have had no difficulty making all my transactions via web, 800-phone, and/or ATMs here. Of course I also opened local CU accounts to facilitate direct payroll deposits by a local company here, but the "remote" place pays much better interest, and offers a much broader range of other services, and better rates on both deposits and loans, so the local CU accounts are used only for occasional/incidental stuff1
1 Our local county treasurer refuses to accept an "out of state" check for vehicle tags/taxes, as one example. While this refusal is specifically prohibited by Federal Banking Regulations, they get by with it, so I use the local account to placate the b.... treasurer. The local CU also "reciprocates" with other Credit Unions to waive ATM fees, which is of some help too, for the rare occasions when one needs a bit of "real money" to keep a pocket warm.
Be aware that high yields quoted may be "introductory" offers, and actual yields over a longer term may be little different than can be obtained from other more conventional places, especially if you look at CDs and/or other "savings/investment" instruments offered by most such places. My "remote" Credit Union offers a couple of account types that pay up to 7.5% current yield, although you have to poke around a bit to get the best rates, and there are some limitations on amounts and "turnover" to get the best rates.
If you have enough to put into long-term savings, an investment broker (esp - in the US - if you can use a Roth/IRA account) will likely get you much better yields than any "savings account," although of course there's some "market risk" to be factored in and it's a little more work to set something of this kind up. There also may be minimum amounts required to set up something.