It might not, TBH, but why carry around an incorrect technical notion that gives you no benefit, even if it doesn't cause you any problems in practice? Maybe my view on this is skewed by the fact that I'm a developer, not a designer...
That said, there are problems that could occur. The main reason to need pixel sizes for things (NOT fonts) is to avoid aliasing effects. For example, 1px is the smallest width you can reasonably make a border. Any smaller and on some devices you may find your border sometimes disappears entirely (aliasing) or is displayed faintly (antialiasing). Any larger and your border may be fatter than it needs to be. If you spurn px entirely (as some people appear to do) how are you going to get this magic length? By saying "0.265mm", perhaps? But that's just another way of saying "1px"!
>If you spurn px entirely (as some people appear to do) how are you going to get this magic length?
You use a high-resolution screen such that 1 pixel is too small to make a line, and on lines thick enough to be visible the effects of antialiasing are subtle enough to ignore.
Well there's not really any other way to ensure crisp rendering. A user with a low resolution screen, even if 1px equates to an actual pixel on their device, might have web pages zoomed in by 15% or out by 10%, breaking all attempts to avoid antialiasing.
That said, there are problems that could occur. The main reason to need pixel sizes for things (NOT fonts) is to avoid aliasing effects. For example, 1px is the smallest width you can reasonably make a border. Any smaller and on some devices you may find your border sometimes disappears entirely (aliasing) or is displayed faintly (antialiasing). Any larger and your border may be fatter than it needs to be. If you spurn px entirely (as some people appear to do) how are you going to get this magic length? By saying "0.265mm", perhaps? But that's just another way of saying "1px"!