Pokemon

So it's just Emerald except modded to include every Pokemon from gen 1-3 as Pokemon that can be caught in the wild?

Pokemon Prism.
Touhoumon
There are also multiple hacks for each gen in which you can catch them all.

Essentially, but what more could you ask for (other than it to be set in Johto instead)?

The starters are Squirtle, Cyndaquil, and Treecko, all the routes have pokemon from every gen, trade and special evolutions have been changed to work with stones, etc

Aside from difficulty/all Pokemon hacks, the only hacks that make a new game I can recommend are Vega and Fire Red Adventure.

Oh and Touhoumon

You had some good ideas but then had to ruin it by going Holla Forums

What if there were a Pokémon game that allowed you to tackle gyms in any order, with every gym you tackle increasing your obedience cap but also increasing enemy/wild Pokémon levels and evolution states?

To keep the story focus, this would be done in bursts. You enter a new area, and end up at a crossroads where you can move to tackle one of three gyms in any order you want. Each path takes you to separate towns/villages/cities/routes and holds their own story events attached to these routes.

The only was it could happen is by doing fan-game made in RPG maker XP.
Romhacks have too much limitations to save 8 different battles for 8 gyms.

Pokémon Mega Adventure is done through RPG Maker XP. It shows that it's feasible to make one using it.

You walk through a field and press A.
Sometimes you need to move the cursor to the right or down before pressing A to pick the rock paper scissors move.
Then you go back to walking around and pressing A.

Romhacks != Game made in RPG Maker XP