An issue with going with llms will be to validate if the behavior described are merely tolerated or if they're correct. Another will be wether something is actually tested (e.g. a code change still wouldn't break the test). Too granular output check would be an issue as well.
All in all this feels like a bad idea, but I hope to be wrong.
Characterization tests ideally need to not be written in code but defined in something resembling a configuration language - something without loops, conditionals, methods, etc. There then needs to be a strict separation of concerns kept between these definitions and code that executes them.
I wrote a testing framework (with the same name as my username) centered around this idea. Because it is YAML based, expected textual outputs can be automatically written into the test from actual inputs which saves tons of time and you can autogenerate readable stakeholder documentation that validates behavior.
It might seem unbelievable but with decent abstractions, writing tests and TDD stops being a chore and actually starts being fun - something you won't want to delegate to an LLM.