As a programmer in an non maintainer / support role, how much do you have to call customers on daily basis?

Zero.

I keep it that way by saying "banned." every time customer support talks about a customer being annoying/dumb/irate.

Or by coming up with positively great responses that would guarantee the player leaves for good.

I'm not a people person. 🙂

On daily basis? If it's more than 0 someone is doing something wrong. A customer shouldn't be contacted more than once a week at max.

I had an analyst to keep customer away from me

There should be a salesperson or someone with customer responsibility. As soon as a customer gets your phone number you're screwed. I usually ask my colleagues to hand over their phone.

In security i only ever give people a direct call if:

A) their shit is fucked and they need to patch by end of business
B) they didnt patch and we took them offline, and now they want me to call them back to explain why they were took down
C) boss or higher needs to know about something ASAP

C is probably out of the scope of the question for most people, but my bosses are actually my primary stakeholders, whereas most of the time bosses or managers are apart of the team

In my last job 3-4 times a week, in my current job not at all😎