It's also a city with 30,000+ undergrads, and another 5,000+ in graduate & professional schools. Even in Baton Rouge Coffee Call does enough business to stay open 24 hours and it's no where near campus. Highland Coffee is busy until they shut down at 11.
Here is the thing. A 24 hour coffee shop will get steady late night business for maybe 2 weeks, three times a year (finals). Other than that it is going to be a haven for 13-15 year olds who cant get into bars. Trust me, if 24 hour coffee bars were money makers (they arent, labor costs mainly, plus prohibitions on business hours) they would be all over the city.
Yes, law school is for dummies.