I'd think so. 3k is so many pixels to compute and send 60 times a second.
But this video says the effect on battery life in their test was like 6%, going from 4k to 800x600. I can imagine that some screens are better at saving power when running at lower resolutions... but what screen manufacturer would optimize energy consumption for anything but maximum resolution? 🤔 I guess the computation of the pixels isn't much compared to the expense of having those physical dots. But maybe if your web browser was ray-traced? ... ?!
Also, if you take a 2880x1800 screen and divide by 2 (to avoid fractional scaling), you get 1440x900 (this is not 1440p), which is a little closer to 720p than 1080p.
/home is not deprecated, it's optional but common. Here is the section from FHS: https://refspecs.linuxfoundation.org/FHS_3.0/fhs/ch03s08.html