In my experience that's not really how it works. Linear resolution might be a fine tool for measuring the sharpmness of lenses but for photographing small subjects with big lenses it's about subject area and pixels on subject.
An 8x10 is 4 times the size of a 4x5 despite only having twice as many pixels in any given dimension. Using your method of selectively measuring only one dimension a person might say an 8x10 is only twice the size of a 4x5 despite the fact that it uses 4x the amount of paper.
A 1.4x tele doubles the size of your subject which is why it needs twice as much light as the bare lens. A 2x quadruples the size of your subject which is why it needs 4 times as much light.
edit: IMO if Canon is going to stop supporting APSC sports bodies they really need a comparable 600mm zoom. 400mm is a great focal length for photographing wildlife on a 7D Mark or with a 5DS/R high body that can tolerate significant croping but it's generally just to short for full frame. The full frame market really needs an affordable 600mm.
We might be talking at cross purposes here. Agreed that doubling the focal length will give you 4x more pixels on target and you can blow up to a larger size, 2x the height and width by doing so. With film you increase the size of a print with an enlarger, but how far you can usefully enlarge is limited by the resolution of the negative. With digital, you can increase the number of pixels 2-4x by using Photoshop if the resolution of the digital image is good enough, and a blown up image from a sharper can be better than one from a longer less sharp lens. It is important to understand what resolution is and how it is limited. What is crucial to me is the amount of detail you can see, and that is determined by resolution.
"Resolution depends on the distance between two distinguishable radiating points..........The resolution of a system is based on the minimum distance r at which the points can be distinguished as individuals."
https://en.wikipedia.org/wiki/Optical_resolution
That is, resolution is a linear measure, based on lateral separation, not one based on area. For a digital camera, three of the factors limiting resolution are the pixel density of the sensor, and the focal length and aperture of the lens.
When the lens outresolves the sensor, resolution scales as the square root of the number of pixels on the image provided by the sensor: double the number of pixels and you do increase resolution but by a factor of 1.414, and not by 2. (It's the Nyquist frequency of the sensor that limits resolution.)
If the sensor outresolves the lens, then increasing the pixel density and putting more pixels on the image will have little effect on resolution but increasing the resolving power of the lens will increase resolution. If the lens is optically good and is not limited by diffraction, lateral resolution increases linearly with the focal length of the lens: double the focal length and you do put 4x more pixels on the image but you increase resolution only by a factor of 2.
The current state of technology is that diffraction is often a limiting factor, and the aperture of the lens can be crucial. If you are above the diffraction limited aperture (higher f-number) then doubling the focal length of the lens without increasing the diameter of the front element (entrance pupil) will quadruple the number of pixels on the image but have hardly any increase in resolution. This is actually the case when you put a 2xTC on an f/6.3 lens on a crop camera or on a high resolution FF like a 5DSR, Nikon D850, a Sony 7RIII or even a 5DIV or R. You put 4x the number of pixels on the image but they are all twice as fuzzy, and you would do just as well by increasing the number of pixels using Photoshop.
I do in fact have a very good Sigma 150-600mm f/6.3 lens for my Canons, and would prefer Canon bring out small, lightweight, high quality primes like Nikon does, rather than another 200-600mm zoom. I am not alone in that desire.