Maybe you have the wrong brokers.
It so happens I do everything through TIAA, because I have employment at an educational institution. This year, I had do to a rollover from my 403b account to a private IRA, and then rollover from the IRA to an HSA (qualified HSA funding distribution). I opened the IRA, did the first rollover, waited for it to settle, then did the QHSAFD. I selected a 100% distribution, so my IRA which started out $5000, actually rolled over $5002. and some cents. The IRA still exists but has zero balance. I don't care if they close it or not, because it was free to open, and if I need it I can just open a new account.
Maybe your bank charges you to open and close IRAs? You may need to find a new bank.
Or, you don't need for the IRA and Roth IRA to be at the same broker to do a backdoor Roth. You can have one IRA open at bank A, and do direct conversions to bank A, B, C or D. You don't need separate IRAs open at bank B, C and D. Even if you want to spread out your Roth money to different brokers, you only need one traditional IRA.
Bottom line is, we don't know exactly what would happen with a one cent balance, but we don't recommend it. Good luck.
