Besides the titles they give you, defeating Master Trainers has two impacts on gameplay:
- Defeating six lets the player battle Red, who will give the player the title of "Battle Master".
- After defeating the first 150 Master Trainers (excluding Mew, Meltan, and Melmetal), a woman in the Game Freak office will give the player the title of "Grand Master".
If you don't care about the titles whatsoever, this means the only benefit to defeating Master Trainers is that you'll get to battle Red.
Master Trainer (Bulbapedia)