Literally in Case Files Volume 1, we see an example of just bad a fight over the Crest can be, with that fake mountain hermit (yamabushi) magus telling Grey, or the other little girl, that his family pretty much wiped itself out fighting over the Crest and he inherited it because he arrived late to the party thankfully. Like he literally got it from his practically burned to death dad, IIRC.
Also, Tokiomi wanted Sakura to have legal protection (a Crest so thst the Association wouldn't just try to take her for a Sealing Designation), actual protection (taught how to use her abilities, and taught well, so that some random crazy magus doesn't just snatch her off the streets and turn her into a pile of parts after "researching" her), and be a wealthy magus much like himself and how he believed Rin would be.
He just had the bad luck to live right next to the magus equivalent of Bill Cosby essentially, dooming Sakura to becoming a more boring character compared to the other girls in FSN.
None of this is hard to understand at all, even with Case Files I would say.