Professional DSLRs can lock the mirror up before doing a shot — to prevent mirror-induced vibration. But as I can see here, cameras such as Nikon D4, while being capable of mirror lock-up, still bounce the mirror up-down on each shot in the series. This doesn't seem useful: the operator doesn't look into the optical viewfinder during the process anyway, so the mirror could be simply locked up, allowing for even more shots per second in the series.
Unlike the very basic DSLR cameras (e.g. Canon EOS 1100D), which are limited in a mechanical way to require the bounce on each shot so that MLU is not available, the more expensive cameras do provide this feature, so they shouldn't have the limitation.
So I guess there's some other technological reason to need this bounce. What is this reason?
This doesn't seem useful: the operator doesn't look into the optical viewfinder during the process anyway
You are mistaken... There are plenty of cases where you shoot bursts on mobile objects (sports, wildlife) and you need to be able to check that you are panning correctly and that they stay in the frame.
On earlier bridge cameras, extracting the data from the sensor would take time and during a burst (at 2 images/second...) the viewfinder would be dark most of the time, with just short glimpses of the subject between frames. This was enough to make them unusable.