There are a few camping mugs with a carabiner handle.
I wonder how it makes sense? I mean wouldn't it be more flexible to just take a separate carabiner with you? You would be able to use it for other things as well as for attaching your mug.
For me it seems to be more a fashion thing than extremely useful.
Of course you can clip the mug to the outside of your backpack or anywhere on the campside but I doubt you really need this. Nevertheless, you can upgrade nearly anything in outdoor business with a biner - it's just cool and you look like a real outdoorsman with all the handy carabiners ;)
Your idea of being able to re-use the biner isn't bad. But than you still need a good way to attach it to the mug. Those "material carabiners" (don't know if this is the proper translation, I mean carabiners which aren't designed to climb on!) are very light, but still it would be cool to be removable in terms of pack size of the whole mug.
One real advantage is that a metal carabiner will rattle against a metal mug. Build the carabiner into the handle and that can't happen.
This rattling may be simply annoying most of the time, but if you're looking for wildlife (whether to watch it or shoot it) is going to disturb your quarry. If you just move around while others are asleep, or trying to concentrate on other things, it spoils the situation for others.