I am aware that a savings account is a limited transaction account and limited to 6 electronic transfer per month, but does Reg. D prohibit a customer from having a debit card connected to a savings account exclusively?

I don't know that debit cards were popular at all when "D" was written. But the problem isn't associating the card to it, it is restricting the transactions that may occur with it. Many banks do not have the system to count the transactions as would be needed. And doing these on an ex-post basis could tie up several FTEs.

Particularly since most debit card systems only allow connection to a transaction account, using a savings account could be impossible for some banks.

The monitoring of activity would, as Andy suggests, be a bear. Particularly since the monthly limit is 3.

Adding to the discussion ...a few merchants do not accept a savings account as a valid account for a debit card transaction. It can cause a major issue to your customer in the usage of it.

We often tie savings accounts to debit cards, but only as a secondary account. That way the customer has access to the account through the ATM for withdrawals, transfers etc.

Our system allows us to specify the checking account as the primary or funding account. Because the checking account is a requirement for the debit card, we have monitoring in place so that if the customer closes the checking account, we contact them to see if they have another checking account to put on the card or if they would like to have an ATM card with just their savings on it.

Just one more perspective...

We, too, issue a combination ATM/debit card, with the potential for four checking and four savings accounts "attached" to it. Of course, the only place the cardholder can access anything other than the principal checking account is at an ATM. And the only place the secondary checking and savings accounts can be accessed is at an ATM that permits access to multiple accounts. This is usually an ATM "driven" by the same provider that we use.