Cooling is very difficult when you're surrounded by a vacuum. Also, without the planet acting as a heat sink, the difference between daytime and nighttime temperatures is staggering.
I don't actually know to what extent radiation hardening is a concern for these satellites. They're well below the Van Allen Belt, so the background radiation is nothing like deep space. Still, it's something you need to consider for systems that are expected to have years of continuous uptime.
(The Russians use commodity PC hardware on the ISS for systems not involved in navigation or life support. But that's a situation where there are people around to hit the power button.)
Not to mention that replacing hardware is expensive, and repair is basically impossible, so there are incentives to prioritize reliability over performance.
SpaceX is actually changing this equation quite a bit in case of Starlink - mass-produced satellites + much cheaper and more frequent launches = replacing hardware gets much cheaper, which means they can prioritize performance over reliability more than it's customary in the industry.
I'm well aware. But SpaceX is heading in the direction of quantity over quality, and banking on the sheer volume of satellites being launched cheaply outweighing any one failure.
In other words, client and server are not both sitting right under the same satellite. The trip to and from LEO is just part of the full route; you also have server to ground station and (in future) uplink satellite to downlink satellite (AFAIK Starlink currently doesn't do that).