I did this for alyph.ai, but was recently flooded with so many browser-using, Turnstile-defeating bots from Taiwan that I had to completely turn off sign ups. It's not fun anymore.
Not even third party login worked (Google, Linkedin, ...) to curb this.
They were logging in, scraping the client API for vulnerabilities/possibilities and then spammed erotic dog poems to Claude Fable until the $5 welcome credit got drained.
Fun New World.
remove free signups
$5 minimum to sign up