Any cactus can be grafted onto any other cactus, and even the most unlike of them grow together. My latest graft was a Schlumbergera truncata scion on an Opuntia microdasys rootstock. This kind of graft is always successful. Why can't garden trees be grafted in a similar way, between genera?
Firstly, different genera of trees can occasionally be successfully grafted. For example, quince, genus Cydonia, may be used as a dwarfing rootstock for pear, genus Pyrus.
However, it is true to say that this is the exception rather than the rule.
In the case of plants in the family Cactaceae, I would suggest that grafting is usually successful for two main reasons:
It is also possible that Cacti readily form callus tissue, which would also aid in the grafting process.
Nyffeler, R., 2002, doi: 10.3732/ajb.89.2.312 Am. J. Bot. 1 February 2002 vol. 89 no. 2 312-326