People that value degrees value the entire package. The full well rounded education.
People that have suffered through those long programs spend their lives looking for ways to use that info, and thus will often come up with stories about how some essay they wrote helped them through a problem.
Everyone pulls on challenges they have overcome to help solve new problems. For many people, university is where they were challenged the most often, and for some the only time they were. So it's logical to pull from those experiences and see them as valuable.
If you went off an joined the peace core and did that for four years, overcoming many obstacles you were go on in life pulling from those experiences and telling young people how everyone should join the peace core.
Personally I loved much of the gen education stuff. Law, History etc. Found the English classes rather tiresome to be honest.
However, it's VERY hard to learn if you either don't see value, or resent being forced to learn it. Based on your post I would say you don't need college right now. Keep working, focus, learn, and enjoy it. Learn as fast as you can. In 10 or so years, when you want to learn something new go then you can go to university and learn something like art history or physics. Go when you actually want to, and you will get something out of it, much out of it.
However asking such a question here is rather silly. Those of us who have degrees with talk of all the value of our tribulations and explain that you should just "grow up" and do it. Those of us that don't have degrees will tell you how wonderful our choices were as well I’m sure.
Follow your gut, you know what you need to do, and what you want to do. Will you get something out of all those GE classes? Sure, some are awesome and will force your mind into new areas. Are you a bad or incomplete soul if you get that in other ways? Of course not.
But remember, most people out there have degrees. And those of us who have suffered through our degrees will often resent and look down on those who try to do go without. Many don't want you to succeed and will try to prevent you from doing so. Keep in mind, If you do, it means we may have wasted our time. So without a degree, you will always face challenges, and downward eyes, and disrespect. Often not warranted or justified, but such is life.
So either join the club, or don't. You can't have a foot in both camps. And either camp will attack you for trying