Well, approval mode solves the problem of people being able to get in without any moderation but it doesn't necessarily stop the issue of being spammed with signups. I think adding a different kind of Captcha (the more interactive one) for signups would help mitigate this issue. It seems that most of the accounts come in bursts, all at the same time so they're obviously using some sort of software to read the image and then pass it.

Would rate limiting help mitigate this, or a stronger bot mitigation at signup? I think it's something that can be discussed especially if this becomes more of an issue in the future.