If you put them in low earth orbit, now you need complex ground stations and/or phased array antennae to track them and move data. And then your cat image generator is on the other side of the planet every 60 minutes unless you have fancy lasers relaying stuff between satellites.
If you put it into geosynchronous orbit, the transmission is easier but now you've introduced a huge delay in your packets.
And I can't even do the first steps on computing what a typical data center needs in network bandwidth. A few terabits per second? A few petabits? More?
How does that introduce a delay?
It’s why satellite internet was usually pretty terrible. A simple TCP handshake becomes a multi-second endeavor.
If you can reach a terrestrial data center in 10 mSec over fiber, the flying data center is 12x slower. And now, like the other replay said, do a TCP handshake and see how long it takes.
A small Starlink satellite burning up once in a while won't destroy the environment, but a multi-gigawatt space datacenter vaporizing in the atmosphere is probably a very bad idea.
What would they be cheaper on? Solar panels are a little bit more effective and they will have a 24/7 coverage if placed in the correct orbit.
However, they would be much harder to cool (space is cold, yes, but heat transfer in vacuum does not work easily and most large structures, such as ISS, require dedicated cooling radiators that take up a large amount of space.) The launch costs would be still very high, maintenance impractical and the large, large surface area of solar panels and radiators would just be primed for being struck by debris.
What orbital data centres are though, is a good dream to sell, a fine way to dismiss environmental concerns of data centres on the ground - “We’re soon going to start putting them in space, but just for now we have to build them on earth. Please approve our requests.”