This use to be true, But not anymore!
No, it is not faulty. The 2x extenders do not work with, or allow for autofocus, with any and all combinations of cameras and lenses.
It still holds true for the OP's EOS 7D DSLR camera.
John Hoffman's unofficial samples proves that a native lens can and does produce similar results, perhaps even a bit better, when cropped to tel-con status as the addition of the tel-con on the lens. So why bother?
The lens is the EF 100-400 L IS.
Without the extender the autofocus options in the Q menu are all operational. When the extender is fitted it only shows a green box MF. Pressing the set button twice turns the box blue but still shows MF. (I'm trying to give as much info here as possible)
I know that AF is hit and miss with extenders but It's as if it's somehow switched off - there is nothing there at all, whatever the apperture.
"The lens is the EF 100-400 L IS."
The 2x tel-con is not compatible with that lens. AF is possible only with a lens that has an f2.8 or faster maximum aperture. Your lens is a f5.6.
With the 2X extender in place, even a 1DX III will not AF with using the normal AF system with that particular lens. With your 7D, AF won't work with the 1.4X either because the aperture rises beyond the f5.6 capability of the 7D as soon as you add an extender. Once your 100-400 is zoomed out to the f5.6 region, it is at the aperture limit of the 7D.
Your 7D turns off the AF function when you add the extender because the camera knows that its AF system won't work with that lens/extender combination.
I have never used live view with a 7D so I don't know what AF capabilities it has in live view. It MIGHT work in live view with that combination but it will work very slowly.
09/26/2023: New firmware updates are available.
08/18/2023: Canon EOS R5 C training series is released.
07/31/2023: New firmware updates are available.
05/31/2023: New firmware updates are available.
05/18/2023: New firmware updates are available.
03/30/2023: New firmware updates are available.