I've heard before that watching 4K video on a 1080p display is still better than watching the same video in 1080p - is that because there's a kind of supersampling going on there?
In a less imperfect world, if you're watching video on a 1080p display, watching a video that is encoded at 1080p will give you the best quality for any given bitrate in any given codec.
Ideally youtube would give three setting choices: codec, (ie, if your device supports decoding VP9 in hardware, it will do that, and fall back to successively worse codecs) resolution, and high quality vs low bandwidth. But that would mean 1) encoding every video twice as many times and using about twice as much total storage. I can understand why they've combined these two separate tunable settings into one resolution+quality knob.
They do separate out codec though; afaik most videos will be available in VP9, h265, and h264. Possibly others.
Fortunately, that’s not how video players normally resize the videos they play. At the very least, players are using bilinear sampling. For the exact 50% downsampling of 4k into 1080p, this means the GPU averages 2x2 quad of the source video texture into one output pixel. This averaging step hides substantial amount of codec artifacts. That bilinear sampling is even borderline free on GPUs: they have tons of VRAM bandwidth, and texture samplers are dedicated fixed-function pieces of hardware.
If you’re using Windows and Media Player Classic, the player has a preference to switch resizing algorithm, Options, Playback, Output, “Resizer” combobox.
The point of selecting a higher definition video stream can be to circumvent bandwidth limitation, if the platform happens to compress too much what it sends by default.