Even assuming an AF system is quick enough and accurate enough, it doesn't have focus points covering the entire picture area. That's how F-L-R came up. The point I want to be in sharpest focus - generally the animal's eye - often isn't at a focus point, and if it is at a focus point it's not there long enough to change to that focus point.
Nothing's perfect, If you focus on the eye, then recompose the composition slightly, you should still be sufficiently in focus. If the central, single focus point is far from the centre of the composition, then that's not ideal. I think Jonathan Wienke did some tests on this.
I'm a firm believer in the Photodo type MTF charts. I find it interesting that certain lenses can be very sharp at wide apertures.
Here's a Photodo MTF chart of the Canon 400/F2.8 non-IS version, probably no longer available. It's actually sharper at F2.8 than at F8, but those who rely upon autofocussing might never realise it.
On the other hand, perhaps this lens is generally very accurate with autofocussing. Who Knows? The 400/2.8 IS is also sharper at F4 than at F8. Photodo have provided no results for this lens at full aperture, but the lens they tested is not quite as sharp at F4 as the non-IS version at F2.8.
The failure of such MTF charts to provide accurate information for the consumer, and presumably the reason why Photodo have discontinued such testing, is due to lens quality variability.
The manufacturer sometimes provides 'theoretical' MTF charts for its lenses, but none provide real, thorough and detailed MTF charts for each lens sold.
The excuse is, it's too expensive. That's a totally invalid excuse. It's a cop-out.
The real reason why manufacturers don't provide a full MTF test of each lens they sell is because it removes their power to bull shit. It's very simple. It's easy to understand. But, alas! perhaps it's not easy for the average consumer to grasp the significance of those charts.
We need more education.