If Parker had not been in such a rush to give away most of US' LGA slots in exchange for a few DCA slots and $66 million, a combined US-AA would have as many LGA slots as DL does now and would have as many DCA slots as US has now. A merged US-AA would have plenty of access to GRU.
So once US and AA are merged, the combined entity will be much smaller than Delta at LGA (whoops) and will be no larger at DCA than US is now (thanks to likely antitrust-driven DCA slot divestitures of an amount equal to AA's current DCA slots). The only thing the airline will have to show for the misguided slots swap is the $66 million. And a much smaller presence at LGA than it would have had if had not been in such a hurry to "win" in its fight with DoJ. Now that's the kind of management any airline would be proud to call its own.