I literally paid extra so that my Dell XPS13 came with a 1080p display instead of the 4k touch-enabled glossy monstrosity it was trying to convince me was a selling point.
Yeah, 4K at 13" is just stupid. My X280 has a 12" 1080p panel and that's borderline too small. That said, my X230 is 768p at the same screen size and that is just awful - nowhere near enough vertical real estate, but it's easier on the old eyes!
If you're doing mail and docs etc then a high dpi with scaling is awesome my 12,5 inch 4k screen was far superior for general use than my current laptops 1080p and things like text looked perfect, no aliasing, so clean and crisp. Only downside on the laptop of more pixels was battery drain brought on from using 4k as a fancy 1080p screen.
Yup everyone is different, but 12" 1080p is decently high dpi, mine is a 14 which is less good, even so I actually run a custom scale on 1080p on my laptop because I don't like the text clarity at 100% there's not enough pixels and looks jaggy whereas a small scale adds some Anti aliasing to the text and smooths it off, by default Windows wants to use 150% which is a bit OTT, I think I do 105%, it doesn't say and I don't want to change it to find out as I tried many to find the sweet spot.