This feels like the right response. I was paying electronically online, but I think that I will go back to sending in my payments using a paper check. I will be sure to include a polite form letter explaining why they have lost the privilege of taking my money electronically. If enough people take this approach, they will probably get their act together in a year or two.
The New York Department Of Taxation has a rule that threatens to fine you if you file a paper return when having the ability to send one electronically. Though to my knowledge they do not actually enforce that rule - just leave lots of warnings around.
Reminds me of those stupid "Must Observe All Warning Signs - State Law" signs that used to be all over Texas highways. I didn't see any my last trip so maybe those are gone finally, but I just passed through the panhandle briefly. They used to be the first thing you would see after crossing the state line, then periodically along all the interstate highways.
Fwiw you can make payments without any account via https://www.irs.gov/payments/direct-pay and also check their status via that page. You just need the account to e.g. get your transcripts.
This would not teach them anything. No, if they want to take away my online account, they lose the right to take my money electronically. They punish us; we punish them.