Why Left Search Buttons are Faster for Users

Without data of any kind, this is merely a hypothesis. I do not buy it; it assumes all mental processing is serial rather than parallel, and takes no account of the fact that as someone types L-R in a text field, the momentum of rightward-moving attention is quite different from scanning static UI elements. Also, it's not hard to see a text field and search button as a compound single UI element, obviating the need to visually navigate it each time.

I might feel differently if I used my left hand to operate the mouse, but then again I might be used to it by now.

Or, have the search box say "Search" in it and the button say submit/go/send, then L-R ordering is maintained without requiring any additional visual fixations (shouldn't there be a third fixation for some users in their revised version when the user returns their gaze to the submit button?).

It seems even more useful to simply do away with the button (as many interfaces do). For instance, Apple's "rounded field" is synonymous with search from its shape alone, though it usually also includes a magnifying glass symbol on the left.