Not issuing new debit card for dispute losses

Is there any prohibition against telling a customer that they cannot get a new debit card after multiple or large disputes?

Not at all. It's a quite common (and sensible) practice.

and depending on the dispute sizes and losses to the bank, may even want to take the logical step of asking them to bank elsewhere

Nope. I've done it several times to customers who can't seem to keep their debit card info safe (or constantly have buyer's remorse as evidenced by the merchant's rebuttal... ). If your lack of sense or lack of morals is costing us too much money, then sorry, no debit card for you.

All of the above. Some consumers are also aware of "small dollar" charges which some banks (we are one) that will simply refund and close because the cost is cheaper than actually disputing. When they figure that out and every other month we're getting the same taste from the dispute - time to go bye-bye.

Nope and ditto this, we do this at least once a week.

Do be careful, however. The EFT Act is subchapter VI of 15 U.S.C. Chapter 41 (Consumer Credit Protection). ECOA is subchapter IV of Chapter 41. Under ECOA §1691, it is unlawful to discriminate against any applicant, with respect to any aspect of a credit transaction "because the applicant has in good faith exercised any right under this chapter."

So, while it may be fine to deny another debit card or even close a consumer's deposit account(s) for repeated error claims under Regulation E, you can't call his loan or refuse him credit based on those error claims, unless you can back up a claim that he made them not in good faith.