I think a lot of banks do allow this sort of transfer (unless it's not permitted under state law). My bank permits it.
Downside risks? The ability to make this sort of transfer has been involved in numerous account compromises. Funds get transferred and then wired out of the country before the customer knows what hit him.
If you don't have robust security procedures to detect and block that sort of fraud, the risk of allowing the transfers goes higher. And in today's environment, a call-back verification process won't cut it.
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John S. Burnett
BankersOnline.com
Fighting for Compliance since 1976
Bankers' Threads User #8