What are the pros and cons? What would you guys do in my situation?
Is your service the sort of resource that the university would happily pay $1k without blinking if you didn't offer a discount? That's the con. (Universities pay for some very expensive subscription services for courses, and sometimes even individual research students can budget that much from whoever's funding their research)
Without knowing more, I'd guess something students won't use anywhere near as many API requests as the professor thinks, and might not be used by students later in life either though...
I would print up some cool stickers of your logo and send them to the professor to handout to the students using your API.
Maybe give them a tutorial on ways to limit/cache API requests so they don't overload your servers.
Good will like this could go a long way leading them to recommending you when ever they can in the future.
Everyone loves stickers they will end up on their laptops and computers and will be a reminder to use your service in the future.