If the IRS were to garnish your accounts, they can get all the account numbers without your assistance. Giving them the information might save them a day or two in the processing.
I am not a fan of giving government agencies sensitive data that they do not already have readily available for historical reasons. The federal government historically have not done well in technical security audits. This is not specific to the IRS and I am not picking on them specifically. More generally this is about technical security audits and not the checkbox governance audits. They are getting better in governance and compliance audits.
All of that said, I am a firm believer in "People can't mismanage, lose or otherwise accidentally leak data they do not have in the first place." I barely trust my bank to manage my bank accounts. Having worked for a bank, I know how antiquated their back-end systems are.
