Many, probably most, Discord servers operate under assumption that discussions are private and are limited to invited users. Making all of these discussions public would make a lot of people very, very unhappy.
But then you run into the problem of having one username across Discord "servers". I don't want what I say on servers with my friends to be easily cross-searchable from what I say on a "server" for some software development library.
I've thought before about how Discord could deal with this. Ideally we would be able to set up aliases, and when joining a server get to select which alias is used. They would have to look externally in every way like they were distinct accounts including when friending or DMing people.
Alternatively, in the UI they could let you sign in to multiple accounts and then provide another layer of tabs to let you switch between those. That would help keep things organized but also can make navigation more difficult by adding another level to the navigation tree.
Easy account switching is the sort of thing that browser extensions would have been developed to cover in the past, something like like RES for Reddit or XKit for Tumblr.
That's obviously less relevant when a majority of users are using desktop or mobile apps rather than browsers, but a plugin interface even for closed-source commercial desktop software used to be far more common than it is now, leaving users dependent on the development team to add features and usability.
I assume this decline is due to security concerns, wanting to be able to develop faster internally rather than needing to continue supporting old APIs for external developers, and marketplaces like Google Play and the App Store not wanting to enable competing marketplaces within the apps they distribute. It's a tradeoff to be sure, and I'm not sure moving past plugin functionality is a bad thing, but I find it a bit sad.
Discord accounts have hidden (until someone uses a bunch of hacking tools known as "dev tools") IDs which uniquely identify an account and never change. The username#1234 stuff is pure fluff. The per-server thing is also just an alias on the server, it still shows the foo#1234 name if you click on a profile.
