I would stop going to THAT restaurant, yes. Especially if they allowed me to provide my payment information in a secure manner, then the next time I visited with a different credit card, made a hard copy of my card number and personal information.
To me, that's the equivalent of what's going on here. They allow me to make a purchase by sending my encrypted payment information to them and then in order to change that to make additional purchases I have to provide my payment information in an insecure manner. I never would have made a purchase from them in the first place if I had to read them my credit card number over the phone.
But that is not the practice you are applying.
I said a restaurant, followed by restaurants (as in, any business that is known as a restaurant).
You said you used your card to make a payment over the phone, and thus will not do business with anyone over the phone using a CC.
See what I am getting at here? You ceased doing business with
all businesses over the phone because you had a problem with
one business, so why would the same practice not apply to restaurants? If you have a problem with one, why would you assume you wouldn't have one with someone else?
My general point is you are assuming all call based CC sales are going to result in the use of fraudulent use of your CC. The reality is, you are speaking with one sales agent who is entering the data into a system (most likely). The only insecure part is that particular agent and their practices. Otherwise, it is no different than entering your CC in a system on a form on the Internet. When an agent is found to be writing that data down, they are fired on the spot, and potentially gone after legally.
In any case, you are writing off payment over the phone when the reality is, you had one bad experience with one bad agent.
EDIT: To further my argument about restaurants, you should know that the waiter/waitress has access to your credit card number, at that point in time. Or the store cashier who needs to run your card through the slider that only they have access to. It may be limited access, but it is the same limited access that is given to the person on the other end of your phone call.