Is Nuzlocking just about the battles or also the rest of the game?

If there was a RomHack which was just about the battles and stripped basically everything else, would this be a game which you would like to Nuzlocke if the fights / encounters are designed well? Or do you also want to collect items, explore the overworld etc.

I was thinking that the RomHack would just consist of a preparation area and a battle area. In the preparation area you can:

- cash in encounters (just get a random Pokemon from a list, you can choose from different lists)

- look at the team of your next opponent

- change attacks, evs (if they are part of the game), nature, items, maybe abilities of your Pokemon for some limited resource.

- choose your team of 6 Pokemon

The battles would be against iconic characters from the series. All Pokemon are Level 100 (or 50?) from the beginning.

Do you think this could be an interesting challenge or would you miss something? When I watched videos of people nuzlocking difficulty hacks, I had the feeling that it is only about the fights. Running back to the Pokemon Center and managing repels seemed to be an annoying necessity.