No thank you.
I regularly wonder if it might not be better for the web if we got rid of pixels as a unit entirely. We can't realistically do that for a lot of reasons, and there are legitimate reasons to use pixels sometimes, but resolution independent font-size and container sizing should be the default. If you are using pixels on the web for font sizes, consider this a public intervention that you need to stop.
The fact that `em` units are not related to physical size attributes is intended. We don't want them to be related to physical size -- what `2em` is saying is that you want a piece of text to be twice as large as the "default" size of the specific font on the platform/device. That is a superior way to think about text size, because as a user I don't want you to try and figure out what the pixel density or screen ratio or resolution of my device is.
Size your fonts with `em` and `rem` units, and size your containers based on the number of characters you want to fit in each line. Don't use pixels. It doesn't matter if your fonts are bigger on Mac or Windows. It is intentional that platforms can size their fonts differently, and your interface designs should take that into account.
If anything, native platforms should be moving more in this direction, they should not be moving away from it. There was a period where you could decide to only care about responsive design on the web, but increasingly you should be thinking about responsive design on native platforms too. And resolution-independent font-sizes based on the user/platform are part of that process.
EDIT: Yes, I'm aware that pixels on the web are not necessarily 1:1 ratios with physical pixels on a screen. That doesn't change anything, pixels are still bad to use on the web. Tying font size to resolution, whether that's browser window resolution or physical resolution, is still equally problematic. And it certainly doesn't mean that we should move in the opposite direction on native devices -- the web's pixels are the way they are because the alternative, being tied to literal physical pixels, would be even worse.