Hi Frode,
The top part of lowercase g of Quadraat has not much in common with the lowercase o.
It is made deliberately like this: the aim was to have the enclosed top-counter as big as possible. So, you have to enlarge it to the left and to the right. You can not go down because that would influence the balance of the lowercase g in a negative way immediately. Back then I had learned this from the work of Pierre Haultin.
Hope this helps,
Fred

Thank you so much for writing, Fred. As I wrote, I was not sure of the origins of this in Quadraat. I have noticed it in many other types too. In my own feeble attempts at drawing a serif typeface, I’ve shaped the head of ‘g’ independently because I find the presence of the flag and the connection to the loop requires it. But then came this idea, that maybe it also needs to be slightly more upright because it is smaller. Like how the diacritical marks are generally given a much more symmetrical contrast (actually, I sometimes think they have more of a reverse-contrast, but that is another discussion). Have you seen any types that employ a less steep axis for smaller sizes?

How would more vertical stress help in smaller sizes?

I think that a less steep axis in the o-like top part of the lc- g is a common thing to do, so its axis is less slanted than the matching lc-o. It is not a law of course. But my feel is that it must be done quite often in faces with contrast. The reason might have to do a lot with balancing the optical axis of the whole letter g.
I might have seen faces with a less steep axis, but in a haste won't recall any.
Best,
Fred

Thanks for chiming in, Fred.

Hrant: I hypothesize that extreme details (which in some cases might be the contrast axis) would benefit from being toned down as the size gets smaller, but I am not concluding – just asking questions: For example, why are diacritical marks often drawn symmetrical, even if the alphabet is not?