I view my readily available funds as not likely to earn interest.
I have a few hundred in cash at home, as I nearly always use CC's it seems to just sit unused, with 0% interest.
Use an ally online account as a bank, it pays 4.2% for the savings account. So keep maybe $10K there as a backup. More if they have a good paying CD (they have low penalties for breaking various ones).
I also have a brick and mortar bank and yes it pays 0% for the checking account, so I only keep $8K -> $10K in there and use it to pay my CC bills, etc. I transfer in money every couple of months or as needed from a brokerage account.