If the mugos are otherwise healthy and alive I don't see why you would necessarily need to get rid of them. Although I find it a little bizarre that the mugos are only now putting out candles, I don't know that it's a great idea to pull out otherwise established shrubs and start all over again. There's also a bit of a difference in mature size for the shrubs in question, so that might affect your decision. Ultimately it's your call, but I would only take the expert's advice as what you could do rather than what you should do.

I don't know about mugo pines specifically, but lodgepole pines (and I thought all pines) have a tap root, which would probably make it difficult to move them successfully. That's my only input.