Probably far from what GF will do with the gyms, but I'd love something based around building your team of trainers to fight the teams of the gym masters.
You could recruit trainers all over Galar by beating them or by completing sidequests (and maybe some main quests), and when you're not fighting at the gyms, you could send the trainers you recruited in different areas of the region to train (catch new pokémon, level up their pokémon, etc.). Each trainer could have a "personnality" that dictates how they build their team and how they battle (will only use water type Pokémon, will play a defensive style, will play an offensive style, etc.).
At the gyms, you would match up your trainers against the gym master's trainers and have them battle, and if your team wins most of the battles, you get to fight the gym master.
I feel like this would be a fun side task to send your trainers to train, and maybe you could even train or progress with some of them at your side.