What's the cap height of Ä? Is it higher than A? Or the same? Will your fixed line height then make Ä intersect the line above? What about あ what's the cap height of that? CJK languages don't even have capital letters... Not to mention the other scripts I'm less familiar with.
This proposal loses credibility immediately for narrowly considering only one language and ignoring the other languages of the world.
Trying to "fix" fonts isn't a one person job. You need a committee of representatives for all modern scripts that are in use. And that's not likely to happen because frankly, is working well enough as it is and disturbing the status quo here is going to cause more issues than it solves, see https://xkcd.com/927/
There are other problems with the proposal, specifying sizes in pixels messes up printing where you have anything from 300 to 1200 DPI. Not to mention high DPI 4K screens. Talking about inconsistency? Try using a 96 DPI screen next to a 168 DPI screen and try to get even the same font to line up... The only way to do that is device independent units and a correct DPI setting for the screen.
I posit that it's not fonts that need fixing, it's the rest of the UI (Windows etc) that need to start correctly using device independent units instead of weird scale factors...
In fact I'm going to go on a rant here... All graphical UIs are doing this wrong, each individual display should use (by default, with override) the EDID reported DPI and all layout should be done with device independent units (RIP bitmaps). This makes everything on the display be the size (in SI units) that was specified and it's consistent between displays of different DPI. On top of that there should be a scale factor to make the entire UI larger for accessibility reasons or if you're using long viewing distances. Scale factor should auto detect if the DPI is too low and be set higher to compensate, this makes text legible by default on low DPI screens like old TVs and projectors that are used for media centers.