"when you have an f/5.6 lens and insert a converter which makes it f/11"
That is the capability of the lens, and yes, at f/11 phase detect usually fails. I thought 2x converters sounded cool, but then I discovered that they add two full stops, and the problems that brings. If teleconverters didn't cause problems, you could just get a shorter lens and stack a bunch of converters on it until you have a nasa telescope. The way you initially stated it, sounded like you thought autofocus would fail if you were shooting at f/11 with an f/2.8 lens, which is an occasional misconception, and not the case.
The degree of blur you can get in camera is minimal? Really? One of us is doing something wrong.
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