Exactly - something difficult to do that not everyone could just do (or rent from a service, or have permanently running). Which is cool.
I'm saying this is an important element to Discord's early success precisely because it understood the gamer audience it was engaging, how it communicated and thought and the tools they were using. Discord allowed people who previously couldn't to "have a server". Which lead to a period of everyone "making" one, and then better ones survived. Not the only factor, but it contributed. I clearly remember how proud people were of their "servers".
I'm sure they knowingly made use of this fact and picked a term that implied more than it does in technical reality because it had social currency. If you play to an audience, understanding what it values and what generates status within it helps a lot.
Back when I _did_ play CS, servers didn't rely on any online component. Many gaming places had their own local servers, and continued to run just fine when the internet was down.
The comments this elicited below harkened back to some great memories of spinning up Half Life and then Counterstrike servers in the pre-Steam days.
Then even more memories from the Steam/Ventrillo/CS days.
Good memories in bad times. Thanks for that and best of luck with midgame!