The reason I wanted to write this is that what I'm doing right now is not a graduate job. You didn't need a degree to apply. Although, my experience at university, and what I studied, has majorly set me up for this. I could not do this without the background knowledge I already had on the issues they deal with, so yes my education has thoroughly improved my chances, but so has connections. Everyone says 'it's not what you know, it's who you know.'
It took me a while after accepting to understand that I had got the job because I was the best person who applied, not because I very loosely know someone there. Self-doubt is really draining. For me anyway, that's why I don't enjoy talking in front of crowds, I'm very scared of messing up or getting something wrong.
The battle isn't whether a degree will enhance you enough to get a job you want, the battle is that your self-doubt probably won't.