Button-up shirts are classics. They may not be trending, but they are not outdated either. They can successfully be worn in all the ways you have described, bridgie--depending on the wearer's style, figure, personality and confidence.
As for myself:. Most parts of my body are a bit long. I am relatively slim, but also curvy, with a considerable difference between my waist width and my hip width. So if I wear a shirt as a top, it has be fitted, never boxy, and it must look fine when worn untucked, as this is how I wear my tops in most cases. The fabric must neither be too stiff nor too loose, and the collar has to look ok when worn open and perhaps popped up.
When wearing a button-up as a top, I prefer to leave a few buttons un-buttoned. (Love relaxed elegant looks.) However, this will create a V-neck, and on me (unlike on many--perhaps most--other women), V-necks generally don't look great, so to soften the lines and fill the gap, I'll always wear a scarf or a necklace.
I recently purged most of my standard-length button-up shirts, as they didn't meet the criteria mentioned above, and as I often prefer to wear other kinds of tops, like pullovers or soft blouses. However, the "right" button-up can look so crisp and sharp--and effectively dress up a pair of jeans as well as dress down a long or glamorous skirt!--so I would definitely be interested in a couple of new ones, preferably icy white and a pastel.
In summer, I love to wear LONG, ROOMY, FLOWING shirts as toppers over sleeveless summer dresses, beachwear, lace singlets, tees, tank tops, etc.