Personally:
• It adds a + challenge, since you're limited to use just a certain type and you need to find a way to cover your type's weakness in some battles. Meanwhile, it gives you a possibility to sweep an entire team depending of your type.
• You can use mons that you never used before! I didn't use a lot of mons in my normal playthroughs because I already had a Pokémon of that type on my team, so it would only bring disadvantage for my team against some types. In mono runs you can pick your favorite type and train your favorite mons of that type;;;
• It adds a lot to your character. In Reborn, for example, all main characters have a type that they focus on, and your character uses multiple types?? That's some huge bullshit right there (not really). So, if you like to give a personality to main characters in Pokémon games, that's a good way to do it.