I'm a huge fan of the idea. I've also been raging for years because of those inconsistencies.
Though I'm not entirely sure this is a matter which can be resolved on the short term :
I'm not sure about this matter, but I think a character's alignement depends on how it's been made to be in the font's files, I don't see any clean way for a browser to change that automatically.
Also, it raises another question, would font designers care if their font's default settings are tampered with (I'd guess that yes, they would).
I think you are missing the main point : default text size IS a size in pixel.
If my memory serves me right, the default text size is 16px for chrome (not sure about other browsers).
Be it rem, em they are sizes relative to an ancestor.
rem being the root ancestor (html selector or browser default), and em being the closest ancestor having an absolute value defined for its font-size property.
Em is great when you want to establish a font size hierarchy in some container for example.
You can test rem by setting media queries defining different font-size values.
You'll see that 1.75rem is always exactly 175% of root element's font-size value.
Though I'm not entirely sure this is a matter which can be resolved on the short term :
I'm not sure about this matter, but I think a character's alignement depends on how it's been made to be in the font's files, I don't see any clean way for a browser to change that automatically.
Also, it raises another question, would font designers care if their font's default settings are tampered with (I'd guess that yes, they would).