I don't think Ride Pokemon or Secret Techniques only one the legpiss Pikachu/Eevee can have are good enough. What I would think would be better is to give certain moves special properties that allow them to deal with the specific situations i.e knowing Slash or Night Slash lets you cut down trees, or most fighting moves letting you move boulders and stuff. There would need to be more to this idea in order to make it work in newer games like restricting certain tasks to certain species that actually look like they would be able to carry them out (no more flying around on Pidgey) and unlocking the ability to do them through the gym challenge again.

I think something like that would combine the appeal of ride pokemon and secret techniques. I'm sure most of you considered implementing an idea like this to give your pokemon more to do outside of battle, but I just wanted to think about how that might actually work.