The question was what do you think is a "reasonable" APY rate?, not what do you think the current APY is.
While most accounts are paying down in the 1.5 to 2.0% range, I think 4% is fair and reasonable.
Yes, they have expenses associated with checks, but at the same time:
They are taking the funds you deposit and lending them out to others and profiting richly from doing so.
Especially when they can milk a debtor for years and years, and if their a solid, very viable institution, then they can afford to have some accounts be delinquent even and run up the borrowers interest rates very high and charge some accounts off if they have to and have the inflated write-off go straight to their bottom line, in effect profiting from money they never even got back. There's only a problem when the number of these types of charge-offs balloon out of control and become disproportionate, then you end up with firms in trouble like so many of them are in now and have taken bailout money from the Fed to keep them in business. But, as long as their losses from charge offs don't exceed deductible limits in and interfere with cash flow, then they are profiting from it even though they didn't receive the money from the borrower. So when they can get outpaced ROI's on lending out a depositors funds and not have to bailout a borrower in hardship when they are getting bailed out, As far as I'm concerned, as long as their in business, they can afford to pay at least 4%.
Heck, with the Rule of 72 your money's doubling once every 18 YEARS. And, by the time you add in inflation and the CPI (Consumer Price Index) effects, and taxes, Your still faced with a losing proposition, hardly greedy! Try to tell the bank that you'll give them 4% interest on money you borrow from them, they'll say NO without hesitating and laugh you right out of the bank. If a higher rate is fair to them, it should be fair from them as well.
And, yes there are Checking Accounts that are supposed to function as a multi-function account with check writing, saving and high yield interest bearing and they are called checking accounts.
I don't believe they should make a distinction between money Minimum and No-Minimum in order to be paid the interest that they would otherwise want to be paid.