Yeah, and the devil is really in the details there; not all context switches are created equal. If you're dealing with less than (rough ballpark) 1000 requests per core per second, there's just no way context switching is going to be anywhere near a bottleneck. Depending on all those details (app/OS/processor/lunar cycle), you may be able to deal with 10 to 100 times as many before context switching is an issue.
Those kind of servers are simply quite rare (IME). Nothing wrong with interesting problems in niche spaces, but it's not something you should be worrying about by default.
(No idea what "big" servers provide public stats, but e.g. https://nickcraver.com/blog/2016/02/17/stack-overflow-the-ar... ) lists a random day for stackoverflow having 209,420,973 http reqests, i.e. a little less than 3000 per second. I doubt context switching is going to matter for them (in the hypothetical world all this was served by one HTTP server, which of course it isn't).