When game is up close, you're often better off shooting thru the mesh than taking the risk of being seen via poking your barrel out the window.
The use of pop-up blinds with shoot-thru mesh has only been a small percentage of my personal hunting, but I usually hunt from them a little annually. I mostly just help other people set them up.
Usually, the mesh is simply removed from the single window most likely to provide the best shooting opportunity. The main purpose of "see-thru" mesh is to help conceal you, and it is a huge advantage in camouflaging you, while still allowing you to see out. It's just a really nice thing you can shoot thru it, with typically negligible issues with POI.
With many these pop-up blinds, you can exchange the mesh from one window to a different one. So if you shoot several holes in the main one you're using, replace it with one of the others (which will often be mostly behind a solid blind wall anyway, i.e. not really being used).
Longevity of these pop-up blinds is commonly only 3 to 5 years.
So when you're throwing an old one away, save any intact mesh windows,
as you may be able to use them on a future blind.