At our Taekwondo school we have about 150-200 students. (It's hard to get an accurate count because there's some students who don't show up to every class, some go on vacation for a month or so at a time, etc). For kids, we have 2 separate white/yellow belt classes (one for 4-7 year olds and one for 8-12 year olds), a purple/orange belt class, a green belt class (which is still 2 belts as it is Green and Green 1-stripe), a blue belt class (Blue, Blue 1, Blue 2) a red belt class (Red, Red 1, Red 2). We also have a couple all-kids classes on the weekend which are used as a makeup day or an extra class.
For teens+adults, it's truncated a bit. There's Beginner (white-orange), Advanced (Green-Red 2), and Black Belt.
Another aspect of my school is the amount of stuff in the curriculum. Required testing material includes memorized punch combinations, kick combinations, jump kick combinations, forms, and one-step defense drills, which are different at every level.
These two aspects (large school, large amount of tested material on the curriculum) basically necessitate that we break up the classes by belt. If we didn't, and we just had 5 classes a day, then instead of being fairly well distributed, we might have 5 students show up to one class and 50 to the next. This is an easy way for us to keep class sizes manageable. There's also so much that's required for each belt test - in addition to other material, like work on fundamentals, sparring drills, games and obstacle courses, etc. - that we can't even cover everything in a single class. If we combined belts then it would be even more difficult.
So this leads me to another con of the separated system: While it does allow you to focus more on the specific skills expected at a certain belt level, it can also lead to a focus exclusively on those skills.
When I was a kid, I was at a much smaller school (although still fairly large, I think). There were a few classes at the main dojang, but my family and I took classes at the YMCA. This class was for all belts. The school also had a vastly different curriculum. There wasn't so much rote memorization of combinations and defense drills. We did more forms (we did both the Palgwe and Taegeuk forms, in addition to Exercises, which were like mini-forms) and we did more sparring.
We did less self-defense, but as it was off curriculum, we could do a wider variety of things. I learned things at this school as a yellow belt that I didn't learn at my current school until red or black belt. But, when I was a red or black belt, we did them every week and built up a proficiency with the technique that we didn't at my old school.
To try and summarize before I go on too long, if you can take the tested material and spend 90 minutes on it, and your classes are 60 minutes long, it's hard to do extra-curricular training in class. But if the tested material can be covered in 30 minutes (at least, what is new material for the belt level), then it's very easy to do other stuff. And if your class is designed around separating by belt level, it may also be designed with more tested material to help distinguish between classes.
On the other hand, doing the same thing over and over again is how you build proficiency, so it can also be seen as a pro.