Quoted By:
How about a game where you play as a fisherman?
Your goal is to become the best fisherman in the world.
You can only catch pokemon by fishing and they will not gain experience through battle so the only way to beat the game is by getting better rods and fishing in different places so you can find stronger pokemon.
Maybe you can fight various trainers because encountering only water pokemon would be boring.
You could also complete secondary goals like catching a specific pokemon. For example, there could be a shiny Politoed rumored to live in a certain pond in a forest that you would have to catch.
As an extra challenge, you could try beating a strong trainer like a gym leader or elite four member, again only with pokemon you caught while fishing.
In the end you will have to defeat the best fisherman at the time and catch a legendary water pokemon such as Kyogre. This would probably be the final challenge since having a legendary pokemon would make the game too easy, though you could still catch something like Phione earlier on.
You could also sell pokemon for money.
I'm not sure about TMs/HMs, if you can buy them you would probably have to grind for money rather than exp when adding a new pokemon to your team, if not you'd just have to rely on whatever moves a pokemon knows when you catch it.