I'll take a stab at this. First there are two ways of looking at this question. One is purely from the perspective accomplishments. The other is from the perspective of quality, whether that be athletic or artistic. I'll try to address both perspectives.
Looking at the question purely in terms of competitive record, the undeniably greatest US pair of all time would be Karol and Peter Kennedy. They were contemporaries of Dick Button, competing in the late 40's and early 50s. They were the first American pair to win a world title (1950) and the second to win Olympic silver. They also won an additional four world silver medals, two North American titles and five US championships. Pretty remarkable to consider that they were part of a spectacular generation of American champions that produced world champs in all eligible disciplines (no ice dance at Worlds at the time). The pair who were likely second to them in terms of accomplishment were Tai and Randy, the second American world champs, two time world bronze medalists, five time national champs, their lack of an Olympic medal hurts their cause (although there was an argument to have them on the podium in Innsbruck in 76). Third would likely be a tie between Kitty and Peter Carruthers and Beatrix Loughrin and Sherwan Badger. Both teams won Olympic silver and at least one world bronze. They also each had a previous top five finish at the prior Olympics. Next would be Jill Watson and Peter Oppegard and the Luddingtons. Both Olympic bronze medalists, one time world bronze medalists and otherwise up and down results. The next grouping would be the pairs who just missed out on Olympic success and/or never rose to the top of the world podium. They include Meno and Sand (one silver and two bronze world medals, 3 national championships and a top 5 Olympic finish in 94; Todd also won a fourth world medal with Kuchiki); the Kaufmans (three time world bronze medalists, four time national and two time North American champs; and Starbuck and Shelley (three time national champs, two time world bronze and controversially fourth in Sapporo). Just behind them would likely be Kyoko Ina and her partners Jason Dungjen and John Zimmerman. With them she won five national titles and two top five Olympic finishes culminating in a world bronze with Zimmerman at the end. Lastly, I would place Inoue and Baldwin in the list based solely on being the last US pair to place in the top five at Worlds (4th 2006).
Now in terms of quality of either athleticism innovation or artistry, the list changes quite a bit and becomes much more subjective. I would place Tai and Randy at the top under those criteria. They were the first pair to consistently perform throw triple salchows and did sbs double axels on and off at a time when double flips were the maximum for most pairs that did not include Rodnina. They reintroduced the same sort of harmonious gentle pairs skating that the Protopopovs made famous. They also had flair, superb technique and a connection with the audience that few pairs achieve. I'd put Meno and Sand second. They had a narrow range of programs and styles, but what they did well was sublime and at times iconic. I'd place the Carruthers third. They has a raw, less refined quality to them that was captivating. They were the kids next door who you wanted to have over for dinner. They were just the most normal, wholesome kids possible. Behind them, I'd rank Starbuck and Shelley. They had glorious lines, a gigantic throw axel, and wonderful unison. Next I'd list Ina and Zimmerman. She was far more consistent with Dungjen, but when they were on, Kyoko and John could be magical. He help to bring out the joyous side to her personality on the ice. Lastly, I'd tie Inoue and Baldwin and Watson and Oppegard. They were both wildly inconsistent teams who tried to push the technical envelope to the edge. They rarely succeeded, but when they did it was beyond exciting.
