Because it doesn't work. This has been tested. It fails because there is too much infrared absorption and "shock kill" destroying the booster structural integrity. This countermeasure was always cavalierly postulated by the bozos at the FAS, Federation of American Scientists, a liberal anti-defense unthink tank (with few real scientists) which the MSM relied on to oppose SDI. Surprising they never admitted when they were debunked.
It is very cheap, too, in comparison with THEL.
Not since it doesn't work.
With shells and mortars it is more tricky as powder gases leave their residue.
Doesn't work for those reasons...and the above. Infrared absorption can't be deflected with mirror finish.
There are infrared/visual mirrors in the lab, and so there are the mirror materials, some of very high reflectivity. IR and visible light lasers have such mirrors as their parts, so right there one has all the necessary coating materials - no need to re-invent the wheel.
Some very interesting physics going on there no doubt.