I feel like many Danes who work in the service sector project this attitude that they're really above the work and that the customers are a complete imposition on their time and energy. That's why I'm always so impressed when I get a really nice waiter in CPH or just shopping at a grocery store like Irma.
I think you're right about the high-end places -- I've only been to one fancy place one (cause, yikes! the prices) and they did act very differently because it was so expensive. But by and large, yes, I agree, they tend to see it more as a "job" than "service."