I am sure someone else can explain it better, but basically in the 80s you mostly only had a choice of 8-bit computers (like Apple, C64, etc.), DOS, Macs, Atari ST and Amiga. The 8-bit machines weren't really networking compatible or powerful enough to do more than 1 thing at a time (128k of ram, 1.02 MHz CPU, etc. though I suppose the 16-bit Apple //gs could have been a contender). Macs would have been way too expensive for this purpose. I don't think boards bought Ataris. A DOS PC could have run a multi-threaded program, but if an issue happened then I guess the whole system would go down. So that leaves the Amiga..
The Amiga was the most performant system, its components (i.e. audio, video, etc.) were all able to work independently of the CPU. It also came with 3 networking APIs built-in (one of which was TCP/IP) which probably helped a lot with the coding.
It was also the only machine with a true multi-tasking OS. Everything else was either co-operative or non.
If an issue happened with one piece, it wouldn't have brought down the whole system because everything was able to run independently.
As for security patches, I was expressing a bit of frustration there because I have seen over and over a Windows "security patch" introduce bugs or break functionality. You didn't have that problem back then with the Amiga. It just worked.
I agree the Amiga was a good choice for the time to administer multiple machines.. and it came with decades of support from the original programmer!