The question of extenders is a question of balance: a balance of cost and size / weight and image quality. I'd much rather capture / slightly crop a bird-in-flight at a native 500 f/4 than start with the same image from a 'doubled' 300 f/2.8L at 600mm. But, if I was cropping the extended 600mm image from a 50MP EOS 5DS R, that might completely change the balance of the variables in my equation.
Extenders, lenses and camera bodies are not static tools with maximized capabilities established in the past. Rather, the boundaries are continuously being expanded. Although my EOS 1v can autofocus at f/8, the sluggishness of the AF with an 1.4x and 100-400 combo on this 1-series film camera is unacceptable for my needs at airshows. If that was the universal performance, I too would be pretty down on extenders. But, when I move the same combo onto my 5DIII, I can track the fastest jets or slower props with no issues. I don't have a family of EOS bodies to provide other comparisons, but I would expect the bodies with the EOS AF system based on the 1DX to outperform other EOS DSLRs (those being the 1DX, 1DXII, 7DII, 5DIII and 5DIV, so far).
The sharpest lens with a sluggish AF would be a problem. A highly responsive AF with a soft lens would also be a poor solution configuration. My earlier link to a prior UHH gallery post included a selection of examples of both birds in flight and planes in flight. All those examples were in bright light, providing the most assistance possible to the camera / extended lens combo. Below is an example looking at the close-up performance of relatively static insects, a more relevant comparison of image details than lines on a chart.
These two examples aren't being presented as 'science'. The original compositions were both cropped from larger original RAW files. The pixel resolution is for online posting, not the full-sized originals. In both situations I was as close to the subject insect as the situation allowed. Both the 180macro and 300 f/2.8L are on the short list of Canon's sharpest lenses and these two examples show very similar results with significantly different focal lengths, shot with the same camera and edited by the same photographer.
My pushback is a pushback against generic naysaying of using extenders. The best option will always be to use the brand's top-line professional body with the longest native focal length prime, sans extender / teleconverter,
where the distance to subject is appropriate for the focal length. But, these 'best' configurations are unrealistic for many of us, and sometimes not for reasons of simply the price. The bodies and prime lenses are large and heavy where combinations of extenders and shorter lenses are a valid option while retaining an objectively high image quality, when using good shooting technique and advanced bodies and the brand's equipment, not third-party extenders.
Birders are not the only ones looking at image details at 100%. Dragging around a 600mm prime would not have been an option for the dragonfly below in a Florida swamp. Using the 300, alone or extended to 420 or 600, gave me a flexible platform for a month of varied situations in GA and FL in 2018. The 180 macro would have been of no use for this dragon given the water hazard and distance to where this insect landed.
There are differences between these two images and both present areas for different technique to improve the final processed result. But, would one try to quantify a percentage difference between the two? Would anyone think there's a native 600mm lens from any vendor that is
25% better than the extended combo used for the dragonfly? 5%? 10%? You might argue that at double the purchase price, an image from an EF 600mm f/4L IS II should be 100% better than this dragonfly example.
Extenders are not a panacea. In my own experience, I haven't found that Canon's various 70-200 models benefit from using a 1.4x or 2x when the Canon 100-400L II is available. If you don't need the f/2.8 aperture, most every Canon shooter will find the 100-400L II to be the better choice, the image quality differences are negligible and the 100-400 offers the option to be extended to 560, also with negligible impact
depending on the EOS body used. But, if your needs require the f/2.8 model for your indoor / low-light work, adding either or both the 1.4x and 2x is more economical than the 100-400L II. A question of balance ...