The ISS is perfectly legal with a license, which I have used to contact them.
You also do not need high power at all, you can do it with fairly low power.
Their personal comms would be illegal to interfere with, and take place on private channels yes.
But they have public comms on the station that operate 24/7 that are legal to communicate with and are on HAM radio bands.. Talking to the ISS is something quite a few hams do every time it is overhead.
@freemo @peterdrake
Could have sworn it was illegal to interfere with their comms because of safety reasons pertaining to the timeliness of vital systems information.