I am not familiar with pearls, but a mechanical sorting mechanism could damage them I think. Also, how is a mechanical sorting mechanism or an electronic counter simpler, cheaper or faster than a photo?
I thought pearls are quite strong, but I learned something today, I just learned that Pearl's Mohs hardness is 2.5 (between gypsum and calcite), meaning very soft in comparison to Diamonds (10).
I had this video in mind: https://youtu.be/nu7snTgSFeE?t=39 They do not look they are gentle with them.
Described method has repetitive manual steps: - put pearls in the trey, - take a photo - take out pearls, - put new ones ...
These steps do not look like much, but if we are talking about amount shown in video can be hundreds of hours.
Phone costs money, and making application costs developer's time and money (so nothing is free) ...
Counting device can be made by Lego, so very cheaply, here is simplistic example: https://www.youtube.com/watch?v=9YguSl_IekQ
Of course device should be made having in mind handling.
By the way application probably has a lot of sense for small dealers, or jewelries,