> doesn't let you sign into different accounts via private browser windows when you have the client running

What do you mean here? I have multiple discord accounts that I have logged in at once. One on the client, one in browser window, and another in a private window, working just fine.

> Another problem with Discord is that its anti-spam measures are making it harder and harder to create an anonymous account

Haven't made an account in a while, what has changed? Used to take only a couple minutes to get an account up and running.