What you would grade with that approach is how well your students can operate a LLM as well as the failure rate of whatever LLM infrastructure the individual student is using. This is usually not the goal of your educational format and hence not what you would grade for - apart from some (meta-)skill courses offered by uni libraries and the like. Those are mostly ungraded, though.

Anyone that knows the subject matter well enough will spot the LLMs mistakes and correct them. If you don't know the subject matter well enough to spot a mistake then you don't know the subject matter well enough.

That outlook is way too bleak. As a person who has taught at universities for fifteen years and has run lots of open educational formats and infrastructure with other public institutions and citizen groups, my experience is the opposite. If anything, the desire to learn and curiosity are among the strongest common traits humans possess. Grades are just a tool and a proxy that most people working in formalized educational settings have to work with at specific points.

I teach mostly smaller courses but my approach to grading has been the same for years: A combination of a semester-long group project (ending in a paper, a prototype and a group presentation) with individual oral exams about aspects of the project and of the lecture. The lecture is flanked by optional TA sessions as well as access to labs which, for most hours of the day, have some experienced/teaching people being around (this results in a lot of ad-hoc learning situations and a general diffusion of knowledge and practices).

This gives me/us a lot of angles to understand what progress has been made throughout the semester as well as to consider and react to individual differences between students. In my book, it’s also resistant to faking it convincingly throughout all modalities. However, scaling that approach to big entry level courses would require more money for teaching than any research group in Europe I’ve ever seen has available.