One might think this would be pro- player choice, but ultimately it would restrict it.
If more than 1 Exotic was possible, enemy health bars would have to be increased significantly. This would promote a meta that would have no close seconds. If you didn't have or want to use said meta, you were at a disadvantage. In future content, Bungie would have to keep that meta in mind and either nerf them or make the enemies strong enough to keep the content relevant and challenging. That would, again, put the players without these weapons on at even more of a disadvantage, lessen the viability of other weapons, or call for nerfs.
That's why.
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If they made one part more easy than they would have to make another harder?