Teleconverters DO reduce resolution and image quality to SOME extent.
Weaker 1.4X TCs do less harm to image quality than stronger 2X. (Even stronger TCs have existed... and typically do a great deal of damage to image quality.)
In general, prime lenses work better with TCs than zooms do.
And there are a variety of grades of teleconverters... ranging from high quality, well matched ones to cheap junk.
The quality of the lens makes a huge difference. An extremely sharp, high quality, prime lens can make very fine images when used with high quality teleconverters.
Some lenses work well with teleconverters or with particular TCs... But other combinations may not work very well at all. For example, someone mentioned the Canon EF 300mm f/4L IS USM doesn't work well with a 2X teleconverter. But I've often used it and find the results very acceptable using that lens with a Canon 1.4X "II" TC (here on a full frame 5D Mark II camera, using a monopod):
Or, the same lens and TC combination on a crop sensor camera (left: on original 7D, handheld... right: on Canon 50D, on monopod):
30% loss of image quality? Maybe in some cases, though that's not a figure I've heard a lot or thrown around personally. I think my Canon 1.4X II "costs" about 5% to 10% and my 2X II around 15% or 20%. I use the 1.4X on 135mm, 70-200mm, 300/4, 300/2.8 and 500/4 lenses (I haven't yet done much testing with it on the 100-400 I got last year). I only use the 2X on 300/2.8 and 500/4 lenses, there's too much loss of image quality for my tastes, on "lesser" lenses and all zooms I've ever tested with it.
Plus, there are many factors that make up "image quality": sharpness, resolution, color rendition, contrast and micro-contrast, evenness of illumination/vignetting, chromatic aberration, distortions such as pincushion and barrel or more complex, among other things.
We get a lot of people asking here about using a teleconverter as a cheap means of gaining focal length. Unfortunately, it just doesn't work that way. There's a very noticeable difference between using a TC on a premium $6000> 300mm f/2.8 and using the same TC on a <$300 "kit" zoom. If a lens is already only marginal in image quality, it ain't gonna improve if you stick a TC behind it. You'll be magnifying any and all of the flaws of the lens, along with the increased focal length.
And, the longer the focal length, the more susceptible your rig is to vibrations that can cause camera shake blur and the more effort a photographer will need to make to get a steady shot. Since a TC magnifies focal length, they always increase the difficulty getting a steady shot. Image stabilization can help a lot, along with a number of techniques that photographers can use to get at least some sharp, usable images.
So, basically, I disagree with much of what the OP stated in the original post about teleconverters. The examples are good, but only tell us about how one particular premium quality lens works with a premium quality teleconverter specifically designed for use with that lens, used in good light at mostly high shutter speeds (1/2000 in one case, 1/8000 in two others... only 1/500 in one). Ideal setup and conditions!