I use my online bank for most of my banking needs. I can do pretty much the same thing with an online bank as with a brick and mortar bank, but without being nickeled and dimed on everything such as having minimum balance requirements, fees for checking, fees to externally transfer money, while also earning higher yield interest (eg. .01% at most major banks vs 3.5% or more with an online bank). Most online banks now no longer charge overdraft fees and may even provide free paper checks. The usual con with online banks is obviously the lack of physical branches. But depending on the online bank, you may still be able to deposit cash (eg. Discover, Alliant Credit Union and CapitalOne allow that) as well as wire money and get cashiers checks. However, I still keep an account at a local bank (luckily with no fees or minimum balances) for the rare instances where I need in branch service. For example, while I can deposit cash into my online account via ATM, I still prefer to do large cash deposits with a human teller just to avoid an issue of getting my money eaten. I also prefer a human teller when wiring money to avoid issues. Or most recently, requiring a medallion signature guarantee when opening a Treasury Direct account.

As for keeping money in these accounts versus investing, the advice on this sub is to only keep as much cash as you need. So basically this means keep any money you will need in a 5 year or less time frame in something safe and liquid like a high yield savings account, while investing the difference. The reason is that the market is volatile and you do not want to be in a situation where you need the money now but due to a market dip, you now have less than when you started. Based on past historical market crashes, it's taken around 4+ years for stock prices to return thus the 5 year rule.

As for safe liquid savings, those don't necessarily have to be in high yield savings, but HYS is the most liquid. If you want to min/max your cash savings and don't mind the extra friction to access it, you can earn more interest by buying T-Bills, CDs and iBonds or signing up for new account bonuses. I typically layer my cash savings. Emergency funds stay in HYS or Money Market funds since they can be access/liquidated immediately. iBonds older than 12 months are also very liquid, but you lose the last 3 months of interest if cashed out before 5 years and are completely unavailable for the first 12 months. New account bonuses, CDs and T-bills bought through a brokerage can be accessed sooner their their mature date but usually involve losing your interest if accessed sooner.