Why can't Bill Pay payments be scheduled with savings accounts with some banks?
For example, the Bill Pay at bank of America doesn't the users to schedule payments with saving accounts:
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In the United States to be considered a savings account the number of monthly transaction is supposed to be 6 or fewer. This is covered in Federal Regulation D.
allow no more than six transfers or withdrawals per calendar month or statement cycle of at least four weeks for the purpose of transferring funds to another of the depositor’s accounts at the same institution or making third-party payments by means of preauthorized, automatic, or telephonic transfers or transfers or withdrawals made by check, debit card, or other similar order made by the depositor and payable to third parties
The bank can then have a policy to disallow connecting a savings account to an automatic payment system. They generally don't allow paychecks to be direct deposited into a savings account. They generally don't allow automatic payments from the savings account.
If you exceed the 6 transfers, they may charge a fee. Or if you do it too many months in a row, they can convert the account to a checking account.