Here are a few times and places I use the 11 fps and bigger buffer:
My youngest kid skis in a half pipe competition several times a year. He does about 7 "hits" in a typical run down the pipe and each of them lasts several seconds from the take off to the landing. There is a transitional period in the bottom of the pipe to the other side between each hit. Within a single hit or trick, he might spin two or three times, sometimes inverted.
So for me, I'd shoot the seven bursts as fast as it could go in hopes of capturing one or two in which his arm or ski is not blocking his face. It is not like I start shooting at the top of the run and keep it down for the entire time, but the bursts add up.
I shot a few eight second bull rides last month, too. The pro rodeo photographers are good at selecting "the" perfect time to shoot, but that takes a long time to learn from what I can tell.
Occasionally, I get to photograph a bull moose crossing a shallow stream. Normally, I time bursts of shots of three to five as he takes his steps forward and as he spashes the water forward. In those cases, he might take 30 sets of forward steps. The D4 is working great for the river crossings. I never have to wait for the buffer to clear and I end up with plenty of shots to pick from. It is almost impossible to anticipate when they will blink, turn their head away, or stick out their tongue. Occasionally, I get unexpected catch light in their eyes, too.
Fighting wild stallions also calls for extended continuous shooting.
So, the need might not be 9 seconds at 11 fps, but instead 150-200 shots over a little longer period of time.