I think pokemon needs to focus on better level design. Get rid of the concept of HMs and Pokeride and give each pokemon one outside-of-battle (out of the box) ability to use on the field. Now every single pokemon (at least in the main game) is a tool that can help you progress and navigate the world, think of it as using a tool in a zelda game.

What if you don't want to keep around a pokemon solely for it's ability? When you catch a pokemon, you'd be given an option to
>keep it in your party (swap if party is full)
>send to PC
>have it follow you around

If you choose to have it follow you, you can use it's outside ability as much as you want, but you can't use it in battle. When you're done with it, you can choose to release it or send to PC. You would also have the ability to use any pokemon from your PC solely for outside use at any time.

Think of how many creative opportunities this would open up. Plus it would give an even greater incentive to catch more pokemon past your main team.