There is no regulation forbidding the use of electric starters. They could fit an electric starter tomorrow (if they could do so without breaking the seals on the engines, which they probably could).
However, an electric starter weighs say a kilo or so. Add in a battery with enough just to power the starter, that's another 500 grams or so. Then try and find a location in the incredibly neatly packaged unit that is a MotoGP engine in a MotoGP frame.
Even worse, you have to subtract the extra drag on the engine an electric starter produces. It's not much, a fraction of a percent, perhaps, but that would be frustrating given that they've just spent a couple of million reducing internal friction of the engine, which the addition of the starter adds.
The main argument, though, is that under normal circumstances, the engine doesn't need to be restarted. The idea is that the bike starts the race and finishes without stopping. The number of crashes is comparatively few, and so the disadvantages of adding an electric starter would massively outweigh the benefits.
The idea may still be a good one, however. Given that the engine starts easily enough once a couple of pins have been inserted into the clutch, if I were Honda, I'd be investigating putting some kind of mechanism in place to be able to do this in the case of a crash. Such a mechanism would have the advantage of not weighing much, being simple to maintain, and not placing a permanent friction load on the engine. Whether Honda are looking at this is another matter.