an f4 and then used the converter either a 1.4X or a 2X then it would not auto focus becuase the "new" fstop would be 6 or or 8
f/4 with 1.4 gives you an f/5.6 and this will be OK with a D30, D60, 10D. With a 2x you need to have a 1Ds, 1D, 1V or 3.
Autofocusing an f/8 lens is slower than an f/2.8 lens ...
I've read the official reason is that Canon wants "fast" autofocus.
My experience is that autofocusing my 100-400 with 1.4x (it's an f/8) and a EOS-1xx takes very long compared to the same lens without the extender (and it only works with the central focus sensor).
You may want to try the "tape" hack to see that phenomenon.
francois