They do that for digital camera displays and it’s super confusing.

That was meant to be in jest - though i would probably chuckle if I saw a marketing banner that said "All new Monitors now with 5.02 x 10^7 pixels"

Eh, you got me. Digital camera disaply resolution is reported like that, worse, they don’t count pixels but “dots” (i.e. subpixels).

Example: the Olympus E-M10 has a 1,037,000 dots display, which means 345,600 pixels, which means 720x480. But all the marketing material (and review websites) reports “1 million dots display”.

If you used megapixels it wouldn't be any worse than camera sensors. I'm honestly surprised this hasn't been done as an alternative to VGA, SVGA, DVGA, WSVGA, XGA, WXGA, SXGA, WSXGA, UXGA, WUXHA, WQSXGA, WXUSXGA, qHD, HD, FHD, QHD, UHD, FUHD, etc. (several resolutions omitted)

A number of megapixels and an aspect ratio would give all the information you need, while boiling it down to easily comparable numbers.

General consumers often care more about physical size than actual resolution. Why else would 1920x1080 pixel computer monitors be sold in sizes up to 27 inches? What explains the proliferation of 15 inch, 1366x768 laptops, or even 17 inch 'laptops' of any resolution?

Definitely, I was just talking in terms of resolution. Megapixels and aspect ratio gives you the same information as width and height (in pixels).

1.05 megapixels vs 2.07 megapixels is a much more obvious comparison to most consumers than 1366x768 vs 1920x1080. One has twice as many pixels as the other.

Switching to that system could even make a few more people realize that a small number of pixels with a huge screen size isn't a great idea. IMO most consumers just see "1366x768" and think "Oh those are big numbers it must be fine."

It's not that the consumers cared more about physical size, it's that they literally didn't know any better.