Why couldn't they tell the government about Magical Girls?
I mean, even if results on some girls "dissapearing", it would give humanity at least some control over Magical Girls and their nonsense.
For example, Remote controled bombs on their soul gems, shock collars, contidioting, etc.
Also, it would be good for the magical girls and Incubators, as the girls will get protected and be given a regular "job" and a secure way to get grief seeds.
The incubators get new magical girls and witches are easly eliminated by their gullibe former companions.
Imagine a whole arc with the goverment using magical girls for wars or against other armies of Magical girls, i think it would make a good spin-off.
As long Homura and Madoka don't fuck up humanity and the universe, that is.
(It's not like Madoka could fix the entropy forever and Homura had any interest on keeping the universe standing.)