Huh, so they do.

Anthropic: https://support.claude.com/en/articles/8977456-how-do-i-pay-... - you can pre-pay and get a hard cutoff.

OpenAI: https://community.openai.com/t/how-to-set-billing-limits-and... - last time I looked OpenAI had a soft but not hard limit, I guess they fixed that last year.

I remember bugging them both about this last year, I need to update my mental model!