My main bank is Chase. Their app is often frustrating for me due to its, IMO, inferior remote check deposit function. I have not had an issue with slow notifications. Their customer service is often disappointing, in my experience.
I set up my Chase bank accounts in such a way that I can maintain very low balances but pay no monthly fees. I also get a free safe deposit box.
I am also a Wells Fargo customer.IMO, their app is superior to Chase's. It takes slightly more effort (10 ATM card purchase or payment transactions vs. 5 ATM purchase transactions) to waive the monthly fees.
I am also a Bank of America customer. I rarely use their app because I usually just park several hundred dollars in an account there without any money going in or out of the account (other than the tiny amount of interest I earn every month). I just go online on my computer to check the account once in a while.
Of the major banks, Citibank has been the worst for me in terms of customer service and its app. Unless I open an Access account (no paper checks), it is more difficult (compared to Chase and Wells Fargo) to get monthly fees waived.
I don't even bother to use the apps for US Bank or Bank of the West. Ugh. And US Bank's customer service? Double ugh.
In my experience, it is much easier to get free accounts at credit unions, though I do not really use their apps.
(Yes, I have a lot of bank accounts.)