It might be developed in a server cluster somewhere, but as soon as you plug a superhuman machine into the internet it will be everywhere moments later.

It's not like it's that hard to hack into servers and run your own computations on them through the internet. Assuming the superintelligence knows enough about the internet to design something like this beforehand (likely since it runs in a server cluster), it seems like the limiting factor here would be bandwidth.

I imagine a highly intelligent human trapped in this sort of situation, with similar prior knowledge and resource access, could build a botnet in a few months. Working on it at full-capacity, non-stop, could bring this down to a few weeks, and it seems plausible to me that with increased intelligence and processing speed, it could build one in a few moments. And of course with access to its own source code, it would be trivial to have it run more copies of itself on the botnet.

Even if you disagree with this line of reasoning, I don't think it's fair to paint it as "*very extreme".