How much would you worry about the height of various elements?
On mobile, a lot.
Think about the target area user has to interact, our fingers are massive and I’m pretty sure you experienced a site that makes clicking on a link/button, while using mobile, extremely frustrating. Add to the fact that some developers think it’s ok to disable zooming.
While, above-the-fold, doesn’t really apply on mobile (since it’s natural to scroll), you still have to think about the performance. Performance is no longer an afterthought, it should be treated as a feature. Due to the fact that Google takes speed into account when ranking, half off your list would go against performance.
I’m all for setting the height of the top section so that you at least control the initial look of your site on all devices.
Stop thinking like a print designer. Why do you want all this control?
Let the site live in the wild. You never know what kind of device is accessing it, so defining any boundaries is just asking for trouble.
Think about vertical rhythm, and let the containers contain…