Remember that the autofocus is only one of two possible reasons that a camera might be slow to capture images. The second reason it might be slow is if it takes a long time to write the images out to flash RAM.

Generally, a camera will fill up its available fast internal RAM and then dump that cache out to the flash card. During that cache dump, it can't do anything.

My camera has a specific mode for taking rapid-fire pictures, where you hold down the shutter button and it goes click-click-click as fast as it can up until it needs to dump its cache. I think I have to specifically put it in that mode for it to work, I don't recall if it automatically does it if I just hold down the shutter button. But I know for sure that if I go click, release, click, release, it's dumping to the flash card each time and will definitely be slower than the fast click-click-click mode.

I think I read something about how some kinds of flash cards are faster than others, and that certain cameras can take advantage of this. Dunno if yours would or not, and I'm not entirely clear on how the feature works or if it even exists.