One of the reasons TI calculators are so popular in schools is because TI works a lot with textbook producers. I worked for a company developing math books for a large publisher and we had a lot of contact with TI. they gave us tons of calculators, gave us pre-releases of new calculators and various other accessories. Thus we wrote our textbook targeting the TI calculators. This is why many textbooks come with TI specific instructions and come with software that only works with TI calculators.

This is probably the reason that many schools mandate these calculators, they're written into the curriculum by default. so it only natural to require them.