I'm a graduate of Columbia's School of General Studies, alongside many veterans and other non-traditional students. I'm not a veteran, but I had many friends that had served. We had classes with younger students from Columbia College and Barnard and I felt like we brought a different perspective to the classes. I learned a lot from my fellow classmates and I feel so fortunate that I had the opportunity.
While I didn't serve, I did grow up with and had close family and friends that were part of navy, army and air force special forces.
The clown you describe does not last long in special forces unless he's a modern day Audie Murphy, Roy Benavidez or Chesty Puller.
In the UK you'd either do college (university) first, or you wouldn't be planning on doing it at all. Some people do in-service degrees but I don't think it's common for large number of people to do a normal undergraduate degree after a military career.
As a result many Americans join the military with their primary intention being to go to school after they complete their service. I believe 4 years is required for the G.I. Bill, but I could be incorrect.