If Harry traded an Obamas invite for the ability to exclude all officials from the wedding including the British PM, then I'm going to score a win for Harry in that negotiation. Well played.
I doubt Harry traded anything.
I don't think there was any intention to invite the Obamas.
Harry and Meghan probably knew that would be open to a lot of media speculation and detract from their enjoyment of their wedding day.
One of the advantages in his position is that he has a lot more freedom to do as he pleases.