Can you create a buffer with a strong acid?
I think the issue with buffer systems is that they are resistant to changes from strong acids/bases in their normal state.  For example, biological systems often are buffered so that they have some resistance to changes in pH, which can wreck havoc on biochemistry.

Recall the basic buffer equation:

$\ce{HA &lt;-&gt; H+ + A-}$

where $\ce{HA}$ is a weak acid, and there is an excess of $\ce{A-}$, the conjugate base. Because $\ce{HA}$ is weak, it is a relative poor proton donor, but $\ce{A-}$ is a relatively good proton acceptor.  So if you now add a strong acid, the $\ce{H+}$ it donates reacts with the $\ce{A-}$ to produce $\ce{HA}$, shifting the equilibrium to the left, rather than to the right as one might expect.  Or perhaps, preventing as much shifting to the right as might be expected. This gets to your issue of buffering capacity.

This line of reasoning does not work with strong acids/bases because they donate/accept protons with gusto, and thus are not resistant to shifting the equilibrium.  You would need to be way at the extremes of pH for there to be a small change to pH, as your graph shows.  In contrast, buffers are resistant to pH change in their normal state.