I think you would always want the option to pay more, but there is a weird dynamic that if the money is available the player will want all of it. It can create a grey area situation that can works against the homegrown team. It's debatable as to whether or not the supermax has truly helped teams trying to retain their players while also building good teams around them. I think having the extra bonus not count against the cap makes it much better for the teams trying to resign their players + build a team around them and the player still gets the money. It would have been super helpful to the Jazz, for example, if that additional money only they could give to Gobert did not count against the cap.
If the "advantage" is purely going to be the ability to spend more money, it's always going to benefit the teams that can pay more money more. I do kinda wonder if the league wants it to be this way, however. The extra punitive luxury tax penalties, for example, were sold as a way to help small market teams but that absolutely worked in favor of the big spending teams.