The newer formats achieve better compression by adding more and more stuff. They're year-long projects to reimplement, which makes almost everyone stick to their reference implementations.
Even most Windows programs (including Windows Explorer thumbnails) don't display images correctly, which is infuriating.
You can't just handle pixels, you need to handle pixels in a context of input and output profiles. That's a pain like code-page based text encodings before Unicode, and we haven't established a Unicode equivalent for pixels yet.
The problem colour profiles solves is about how the monitor should display those colours. It’s so that what you see on the screen is going to be exactly the same shade of CMYK as what gets printed.
It’s a big problem for magazine (and equivalent) publishing. Movies too. But much less of an issue for other media industries which are targeting end user devices like smart phones and laptops.
The equivalent in typefaces would be the font rasterisation itself (like Microsoft Clear Type) rather than code pages.
You need a monitor profile because the display protocol takes dumb numeric values that are interpreted in monitor-specific way, instead of being sent in some universal color space, and converted to monitor's internal format by the monitor itself.
In this analogy monitors are like pre-Unicode printers, where characters were just bytes, and the bytes mapped to whatever 8-bit language-specific font the printer had.
This isn’t true. Particularly with monitors where people can adjust the contract and brightness.
The reason colour profiles exist is so that computers can be calibrated to support the monitor output.
You are also ignoring the fact that environmental factors can have an effect too. Ie how the room is lit.
Comparing something standardised like writing glyphs with something highly individual (monitor calibration) doesn’t make a whole lot of sense.