1080 is a measure of one axis. 1×1080 is still 1080p.
1920×1080 isn’t “1080p”
“literally any number” x 1080 is 1080p.
“sued into oblivion”
I see what you did there.
1080p means it has 1080 lines. Each line could be 1 pixel wide. 1×1080 is still 1080p.
That’s how old 4:3 content is still "1080p" even though it’s not 1920×1080, it’s 1440×1080.
"4k" has the rotated problem. It’s 3840 wide, indeterminate height. So 3840×1 is still "4k". Technically that’s "UHD" since proper industry 4K is 4096 wide. (But, again, no height requirement, due to film aspect ratios varying) However, all UHD TVs are calling themselves "4k" when they’re not quite there.
So if anyone has a beef, it’s with the standards body that settled on the designation 1080p. However, there really isn’t a way to get around this when there exist (and always will exist) different aspect ratios. If you pick one axis to measure, the other will always vary. Always. It can’t not vary, that’s what aspect ratios ARE.
So Sony stuck with 1080p but it’s anamorphic, and apparently it’s also anachronic, which is fascinating.