So here's my thoughts as a farmer with 300 head of beef cows:

Old style hip roof barns were like that because before balers, hay had to be put up under cover, and it was put up loose, not baled. You needed these massive lofts to put up any sort of useful amount of winter feed, even if at that time, a large herd was 30 beef and a couple dairy cows. Many of those lofts were used for dances as well if they weren't filled with hay. As bales became common, you didn't need to put as many away in these lofts, and if you did fill them with bales, you'd collapse the loft because they were built for loose hay, not bales.

So bales started be stored outside, either exposed to weather or under a roof cover or tarps. Then round bales came about and they don't really need any sort of cover because they shed water fine because of how they're wrapped.

Modern barns might be 12-14' inside, but that's because they only get used for a couple months of bad weather calving and most cows in areas that are just cold but not rainy make out just fine outside, and would be too hot inside, not to mention spreading diseases. So these barns will often get used for equipment storage and to make them easier to start in winter. The attic will be unused. The extra volume is nice for evening out humidity, but you can also run fans if need be. Many cattle barns are only big enough to run whatever equipment you need to feed and clean it out.