> Like I know the new satellites can use beam forming to increase power for some large area for military use
No, what you think you 'know' is plain wrong. Usually when discussing satellites, we're talking about a directional antenna that focuses a spot or wide beam for broadcast. A spot beam allows you to target a particular region, DirecTV uses spot beams to provide local broadcasts to general regions of the US. The military uses M-code shit on GPS with a directional antenna for the same sort of use case.
Beam forming is a different concept where you get creative with multiple antennas broadcasting at once and exploit signal cancellation to improve the data rate by shifting the phase between them. It does increase your received signal but relies on the receiver transmitting information back to the satellite (which is not going to happen for GPS, at least not the vast majority of consumer equip). Beam forming discussed on HN just last month: https://news.ycombinator.com/item?id=22784132
> What's stopping us from deploying 10KW sats?
Sat power is around and above that already, it doesn't make sense to increase the spot transponder ERP too much or you end up with issues like interference with adjacent bands since RF gets trickier to filter the higher the power it gets. Keep in mind a comm satellite usually has lots of transponders using maybe 100-500W each, so it adds up to some geosynchronous ones being like 20kW total consumption. Smaller LEO ones obviously not going to be close to that.
GPS released a paper about interfering with itself: https://www.gps.gov/multimedia/presentations/2010/10/ICG/bet...
Communications history is littered with failure stories of people who wanted to throw power at the problem, when they only needed to find ways to listen better.