You are quite wrong, ignoring both the megapixel wars and how video encoding works. There are
enormous trade-offs involved here, and one chip may produce files twice the size and half the quality of another chip
even with the same sensor and lens—to say nothing of the variation possible in sensors and lenses! If I record 1080p on my Surface Book with its rear-facing camera, for example, it runs quite a bit hotter than a typical phone with very similar optics, but produces substantially better quality for a given bit rate—in doing rough visual comparison earlier this year, I estimated that it was producing obviously better results at a quarter of the file size, comparing it to a mid-range phone of a generation two or three years newer than it.
Also the other aspect of resolution not being everything is the optics; my Sony α6100’s 1080p is miles ahead of most phones’ 1080p in quality, and I think there’s a high chance it’d be better than a $100 4K video camera’s 4K.
In short, not all 1080p or 4K or 8K or whatever is created equal.
One other thing to remember: all else being equal, 8K video will be consuming four times as much power and generating four times as much heat as 4K video, which will be consuming four times as much power and generating four times as much heat as 1080p video. (Of course, all else never is equal, but it’s a fair approximation, especially within the context of a single device; but when comparing between generations, as part of quadrupling the pixels pushed, they probably put more effort into efficiency to try to balance power and heat things out too.)