Arthur absolutely has a place in our team. His role as a "controller" is needed for any side especially a team like Barca that wants to control games. If the attackers in front are creative then he doesn't need to provide a killer ball all the time, but he should still work on it. His defensive skills aren't the best but having two midfielders next to him that are good in that area can mitigate that. He just helps provide the match control and ability to play out from the back. It means Messi can stay further up the pitch and focus on creating/scoring in the final third.
Busquets/Arthur/de Jong is a combo that will suit Busquets and maybe prolong his career, but imo he's mostly finished already. It's still a good set up for most liga teams where Barca can use them to have match control and let the forwards create in the final third. It lacks incisiveness and physicality though.
de Jong/Arthur/Vidal (de Jong as the DM) is a combo I like because it provides match control and is defensively solid with de Jong and Vidal. Great for big games and in Europe. Vidal also adds physicality which is lacking in the first set up. It lacks the "penetrating" midfielder but Barca will have to rely on the front three.
In an ideal world there would be a third midfielder to pair with Arthur/de Jong who is physical/decent at defending and adds some penetration/forward runs. A box to box player.