What's wrong with 一个年? From what I can tell, 一个年 is completely wrong because you can never use a classifier together with 年. The situation is different from a phrase like 一个朋友.

My question is: why? Is there a reason why 年 is different from 朋友 like this? Are there other nouns which behave like 年?

Or is 年 really syntactically more like 个? Is 年 actually usable as a measure word? Can you for example say 一年时间 or 两年工作?
You cannot say 一个年, but you can say 一个年头 

The difference between 年 and 年头 had been explained here  Understanding 年頭 in context

Yes, 年 itself can be a classifier  '一年时间' and '两年工夫' are both valid