Someone else suggested it may be similar situation to galls..
They could be right.
A lot of it comes down to compatibility, two species that can grow as mixed in-vitro cultures together without a zone of inhibition are more likely to be graft compatible or at least not immediately incompatible.
If I recall properly a gall is a formation where an organism interfaces with a host plant to form a specialized cyst-like structure composed of callus-like tissue, so the suggestion that cross species grafting is gall-like seems valid to me.
There is a cancer-like element as well, where a scion is like-unto a foreign tissue that is part of yet not part of the original organism that obtains energy and sends chemical signals through the host. The host meristem typically is able to monitor the entire plant via various network like chemical systems. In my experiments plants even detect and reject, in many cases, fruit that is not pollinated by the proper plant. People have used hormones to prevent this type of tissue rejection and get certain hybrids to work more often with Ipomoea batatas as an example.
The need of the meristem to communicate back and forth with the cells via multiple signaling pathways is likely the primary reason that grafting success is almost entirely limited to plants of the same families. Gall formations involve special hormones, in many cases, to keep the tissues alive and prevent rejection by the host. It isn't entirely different than the situation with organ transplants and needing medication to prevent rejection with our own species. We even graft pig parts to humans successfully using this type of treatment.
Since protoplast fusion hybrids of plants in distinct families are known, it may even be possible to directly perform meristem to meristem grafts or initial transplant grafts with initials being the active special cells in a meristem that monitor the plant. A chimera is a mixed meristem plant and there should be some fairly simple ways to induce them with the right methods and tools. A bit of callus tissue from one cactus or plant might be carefully excised and placed in the meristem region of another plant with a potential chance to induce a chimeral meristem. A crested plant with a long meristem might be far easier to work with in this regard. I've had no success with the single meristem to meristem graft I tried recently but want to try again later when the weather is more plant friendly outside.