I haven't gotten into Discord yet. Isn't it a pain that there are so many Discord servers and you can't just have one server with all the channels (ala Freenode)?
It is normal to be connected to multiple servers at once, and the UI makes it easy to keep track of them.
As the other commenter said, it is much better to think of each server as a channel. A Discord server is typically dedicated to a single topic or organization. My old World of Warcraft guild has a Discord server. On that server, you'll have separate channels for general chat, announcements, and several voice channels for groups.