Credit cards do the exact same thing. Sure they will deactivate it, but if you put a charge on it for 60 days it is reactivated. This was a pain for me because almost all my bills are automatic payments.
Ask for a new one and then cancel it. All those automatic payments will bounce off the first card and you won't have that problem anymore.
Doesn't reporting your card stolen (which is required to get a new number/card) adversely affect your credit scores?
Hasn't yet for me. Never heard of that, either. But I looked it up and that can happen when the bank makes a mistake and lists your new card as a new line of credit. So you could fix it through the dispute process, which is painful. Whether the new account is "adverse" or not depends on your individual report.