Binge drinking in college usually leads to students doing worse academically. Students are out late at night drinking and don't have time to complete their academic assignments. This leads to handing in assignments late and even failing and dropping out of classes.
Unfortunately, these private colleges aren't as concerned as they should be with students failing course or even dropping out altogether as long as they are still getting their money. This leads to less regulation of college drinking and less focus on improving the actual learning environment for students.
Privatization clearly isn't the sole cause of binge drinking in college because I believe the bigger reason behind binge drinking is a social/cultural aspect, but privatization certainly isn't helping the situation.