I think I understand that, but wouldn't you think that adding an "unknown fuzz" by sharing computation on 1-or-many threads makes it harder for an external party to do timing attack?

The attacker now has a lot more possible outcomes depending on the number of threads handling that packet. I seems, on the surface, as if more threads add complexity to the attacker.

Debugging multithreaded code is much harder than single threaded, especially because of all the race conditions that can happen: it makes our brains burn hot from all the possible outcomes from identical runs run one after the other. My intuition would lead me to believe that this complexity is also now added to the attacker's side - but perhaps I'm missing something.