If someone knows the specifics on them I would be happy to know, but I feel like there is a lot more heat generated in a data center, of any useable size, than could feasibly be cooled using radiators.

I would like to add a bullet point to your issues since I'm not sure solar would be good enough to sustain such an orbital. Once again I am only surmising and would like to hear if I am way off base.

they will need to be constantly replaced.

This is the funniest part. Can you imagine completely rebuilding the average datacenter every half-decade?

1. The costs (monetary and environmental) of launching so many new satellites,

Fraction of damage and cost of earth based datacentres.

2. Large-scale computing technology is untested in that kind of environment and will likely encounter a number of issues and unforeseen problems (so more launches until they get it right),

We've been putting computers and satellites in space for decades.

3. Additional radiation will increase errors, so they will require a more robust design with more redundancy than Earth-based systems,

That's what shielding is for. We have probes still working after 48 years in space.

4. If they’re in a low orbit similar to Starlink satellites (which have an expected lifetime of 5 to 7 years) they will need to be constantly replaced.

so place them in higher orbit.