We have carried our very big and heavy annexe across the country on several trips, just in case, and never used it. We have only really used it when we set up a base camp somewhere for a week or more (which has only been twice), and even then we often don't use it.
They are great in theory, but in our experience, we've found carrying the extra weight and the time to erect it all a burden.
As is lifting it on and off the camper every time we set up and pack down when we're touring.
I should clarify though, our Mountain Trail Extended Expedition camper has a very large tent and annexe, with the heaviest weight canvas on the market. Our annexe actually has the mesh permanently joined with the canvas walls, so we can't just take the mesh walls.
If we had the option for just taking the mesh walls, we may feel differently, but in all of our travels we may have just been very lucky timing wise, but we've never found anywhere where the critters were so bad that we needed the mesh screen protection, and that includes The Kimberley, Cape York, Fraser Island and Outback Australia.
It probably depends on your travelling style (1 night stops or several days in each place) and your tolerance levels for bugs etc...
Karen