What you have is a "perfin" or a stamp perforated with initials, usually as a security device. It is also cancelled with a nice date stamp. It is not "cancelled by perforation." In general, a perfin that is also cancelled isn't too rare, but the perfin itself may be something that is uncommon, so it could be of interest to some collectors. I'm not an expert on Belgium perfins, so can't help you out there.
I have to point out that using a coin holder to display the stamp isn't really a good idea. It isn't really locked in place, and can move about. It is also creased in multiple places, and the perforations are bent in at least two places, so that it not good. My recommendation is to carefully remove from that coin holder and place in a stamp mount.
When you say that it, "is incredibly rare due to the fact no one cares enough to document these types of antique cancellations", is sort of circular reasoning. Maybe no one cares enough to document them because they are very common and not worth the time?
The link that you provide actually has the JPB perfin illustrated, showing two different patterns for it. Therefore, one can assume that the JPB perfin itself is very common.

In any case, I'll let others comment also.