blowing up a satellite in orbit is a massive escalation over even something like a commando raid -- i believe it would qualify as a violation of outer space treaty as well. a great deal of 'space junk' was generated by china's (one, individual) test of an antisatellite missile in 2011, and it caught a lot of critical international attention over it because it puts other satellites in danger -- thousands of tiny pieces zipping around like a 3d minefield. this hazard would potentially apply to US military satellites as well.

besides this: there are many, many ways to spy on satellites. the US is believed to have at least one satellite that sits 'above' a major middle eastern comms satellite with a football field-sized antenna, passively snooping everything shot at it. you can encrypt it, sure, but do you have high enough trust in your crypto implementations to deal with an adversary like that?

what i'm getting at is, i don't think they would shoot down the satellite.

Try that with the moon.