Yes, since neither GPU drivers nor most displays currently support integer scaling. See http://tanalin.com/en/articles/lossless-scaling/ for more a more in-depth explanation.

Fascinating. I assumed that an even multiple is all you need to ensure crispness.

I mean would the display need to know - just GPU drivers should be able to send a 4k signal that has 4px squares each of one colour? Interesting though.

It doesn't need to, but it would suffice in case your GPU doesn't manage.

Well they're usually bigger. IMHO 1080p for monitors maxes out at about 22-24" before it starts to look blurry, after that you want 1440p, until about 28", which is when 4k starts to make sense.

You may need "font smoothing" enabled.

Of course it's worse, since you have more pixels than image data.

By that logic Apple's Retina displays would be worse than non-Retina displays. Down-sampling decreases eye strain and makes the image smoother. It is only an issue when dealing with fine lines that our eyes watch very closely, such as in text.

If you turn your apple retina display to 1080p mode, then I would think it's not that good when there's a 1:1 correspondence between physical pixels and pixel data. However when the size stays the same, I wouldn't expect much difference.

A 32 inch 4k display downsampled to 1080p, well... :)

A down-sampled image has less noise than an image in its native resolution. You can experiment on your own monitors if you don't believe the theory, just remember to use font smoothing for non-native resolutions. You can also ask about it on the appropriate stack exchange, it is a frequent topic of confusion.

This is one of the advantages of shooting at a higher resolution than the intended target delivery resolution. When downscaling an image, the noise gets 'averaged' out of the image. For HD 1920x10280, a 2.7K resolution was a good choice before having to jump all the way to 4K. There's other technical reasons as well for shooting larger than intended use, but just re-enforcing the 'noise removal' process of downscaling an image.

depends on the density - if both monitors are the same physical size, there should be no difference.