Why would I want my satellites to be 'stealthy'?

Solution 1:

I do not want to spoil the game much, but in late-game you will have certain big UFOs turn up that you may or may not be ready for. These will not be taken down by your interceptors so easily and a few showings from these might even lead to your entire Interceptor fleet getting wiped out or them being just plain useless.

This will cause you to leave some of these UFOs alone without doing anything. This usually has a repercussion of them attacking the satellites. A successful satellite take down will increase panic in the country by 2 points. Again, this may or may not overwhelm you with panic-stricken countries, depending on how well you stand in game.

So when you do reach this stage you want to have those satellites survive so that they do not drive panic up anymore than you want. This is the only reason you would want stealthy satellites.

Personally I would rather have satellites in stock ready to launch so that when one gets taken down I can launch another and get panic reduction in the area. Especially effective if panic is almost maxed out in the area.

Solution 2:

UFOs can attack your satellites if you choose to ignore them or unable to shoot down. There is a chance that UFO will come to destroy one of satellites on that continent. With "stealth satellites" there is a chance that sat not being detected by this ignored UFO.