They act as a massive supercomputer
I think you massively underestimate how massive a massive supercomputer is, and most importantly, how massive both the power requirements and the cooling requirements are.
Remember, a computer essentially turns electrical energy into heat, so not only do you have to put an enormous amount of energy into the computer, you also have to put another enormous amount of energy into removing the energy you put in.
The biggest solar arrays ever put on a spacecraft are the ones on the ISS. When the installation of all 6 iROSAs is finished, they will generate 215 kW of power. The most advanced space-based nuclear reactor, the Kilopower project still under development, will have a 10 kW version with a mass of about 1.5 t, so you could strap together 20 of those and get a similar power output as the ISS solar arrays, which are however at least twice as heavy.
The most efficient supercomputer in the world, according to the Top500 organization's Green500 list from November 2022, is the Henri system which achieves 65.091 GFlops∕W.
Assuming we could have 10 times the power of the ISS and assuming we could use their full power only for computing and not for cooling, and assuming we could build a supercomputer 10 times more efficient than Henri, that would give us a computing power of ~1.4 EFlops.
That would put the computer barely, but just barely at the top of the current Top500 list. So, you would think that putting a supercomputer in space would be quite reasonable.
However, you have to consider the following:
- I assumed that we could make a supercomputer that is 10 times more efficient than the current most efficient supercomputer in the world.
- I assumed that we could generate 10 times as much power as the current most powerful power generator in space.
- Supercomputers on Earth get faster over time, whereas your space-based computer can't be easily upgraded. E.g. the previous Top500 record holder only spent 2 years at the top of the list, then it was overtaken by a computer that was 2.5 times faster. It took only 3 years to get a 10-fold improvement in performance.
- Supercomputers on Earth get more efficient over time. It took only 8 years to go from single-digit GFlops∕W to the current record of over 65 GFlops∕W.
So, even with our completely unrealistic assumptions about making the computer 10 times more efficient than the current world record and generating 10 times more power than the ISS, your supercomputer will essentially be overtaken in less time than it takes to build and launch it. Based on current performance trends, even the 500th supercomputer on the Top500 list will overtake yours in the 2030s.
Just as an example: the SBC-1, when it was launched, would have placed around 130th in the Top500 list. When it returned, only 1.5 years later, it would have barely made it in at 400–450th. Your 20 SBC-1s have roughly the same computing power as two PlayStation 5s or Xbox Series X, or a single top-tier gaming GPU.
And remember, even if your completely unrealistic supercomputer is, for a brief moment, the most powerful supercomputer in the world, it is still only one. Whereas here on Earth, there are tens of thousands of supercomputers.
Also, we haven't even talked about mass yet. A 200 kW version of the Kilopower would probably have a mass of 30 t, and that's just for the power generation. We still have no computer and no cooling.
Lastly, these kinds of computers are not very small:
Note that that's only the compute nodes. Not visible in the photo is the power distribution and the cooling systems.
Another problem with your idea of a "distributed" supercomputer is that one of the major problems with current supercomputers is communication bandwidth, but even more communication latency. IOW, much of the work on current supercomputers is put into how to put the compute nodes as close together as possible. Your idea of distributing the compute nodes around the orbit will devastatingly cripple the performance.