Quite frankly one of the dumbest things I've ever heard. You're unnecessarily paying more for a service.

It gets obnoxious

It really doesn't.

Almost like you did it just for the discount.

Bruh. No-one thinks this. In what world would someone take up a job in the military solely to save £10 on a meal?

So if you’re constantly asking, you kind of look like a cheapskate

Dear lord this is so extra. It's not cheap, it's logical.

but we’re not going to bother people.

Bother people? You're at a restaurant and you ask "do you offer a military discount?" You're not burdening anyone. They most likely already know whether they offer a discount or not.