Satellites experience time dilation because of their orbital velocity and gravitational field being significantly different at their altitude. Without accounting for this, the clock drift would become unmanageable and Newtonian models are insufficient to correct for it.

You're right that the majority of Einstein's theories were ultimately thought experiments but getting the parameters correct involved a lot of measurements and experimenting, to get to where tech like GPS and StarLink can be accurate. We were also looking at far away stars for centuries before Einstein so that he could have the environment for his ideas to be discussed, which I was including in my phrasing "looking at things light-years away."

I wasn't saying it to start an argument, though. I wanted to counter the rather dismal view of "why do we need radio telescopes."

Einstein developed a theory that includes General relativity and special relativity. Experimental results confirms both of them, with special relativity being the easiest one to understand the consequences of. Without experimental confirmation, neither theory would be valuable.

Communication requires accurate timing. Time dilation occurs between Earth and satellites, a phenomenon that isn't part of Newton mechanics, so relativity is indeed involved.