It's so logical, they multiply errors by their extender factor. But is it really so? Why do 1.4 extenders have hardly any effect on sharpness, whereas 2x extenders are often considered to be marginal? If 1.4x are so great, maybe stack two of them to get to 2x instead of using a 2x. And that doesn't make any sense either.
Apart from that, it should be possible to design a teleconverter that improves sharpness, because additional lens elements can do that.
If you are going to be cropping, you are also multiplying the lens 'errors'.
So for the vast majority of scenarios, it's a comparison of crop vs TC.
So take a shot without TC and then another with 2XTC.
Crop the first shot to 3480 pixels wide (in the case of R7.)
So now it's 8.1mp bare lens shot vs 32.5mp for the 2XTC shot.
Unless you're using a 400 2.8, or shoting a static subject using a stable tripod, you are probably now compromised by much higher ISO, or much slower shutter speed, or diffraction, or a combination of those.
Then, we usually judge the results using a display and often with our own flawed method of judging. (I include myself as being less than expert)
Some would say printing to compare would be the 'proper' way to evaluate results but prints are not necessarily the intended output.
When I first got my R, I stacked 1.4 and 2XTC, using 12mm extension tube between them, on Sigma 500 f4 and was surprised at the quality. IMHO still looks good after cropping. I used Gitzo 5 series tripod and big ball head which is still inferior to my usual beanbags on a boulder method, but still very solid for tripod.
My beliefe is that TCs have a higher potential for best results compared to cropping but also make achieving best results more difficult which is why many consider TCs degrade results too much.
