Ironically enough, our lecture halls were simply not big enough. The space capped out at around 300-600 people and for popular topics such as programming 101 every semester would easily have 1500+ enrolled.
The difference is that in Europe, you apply to take a specific subject at university, like Computer Science, and there are only so many spots available so that effectively caps the class sizes. You don't have a bunch of other people taking the class that are not working on that specific degree.
This is also the case in the US. The majority of college courses are limited to people within a given major and can't be taken by outside majors with limited exceptions.