First of all, the US advantage in agriculture was mostly due to resources such as the availability of large amounts of fertile land/person. Yes, the cotton gin was important. Yes a lot of improvements came from the USA. But this is no different than successful technology transfer anywhere else. People who have problems, find clever solutions to them. This becomes the foundation of long-term growth in innovations.
Secondly, you are massively underestimating Asian innovation. Almost all global manufacturing of key technologies, such as RAM, has almost entirely moved to Asia. Moore's Law has not slowed for those technology. There is lots of innovation going on in those fields, and it is all Asian at this point. Mostly covered by trade secrets rather than US patents, but it is still real and your computer wouldn't run without it.
Did you hear that Samsung recently got criticized for deciding to budget more on marketing than R&D? They did. When was the last time that you saw a US company criticized for valuing marketing above R&D? What does that say about the innovation culture in South Korea vs the USA? (Yes, innovation in China and India are behind South Korea - but 20 years ago nobody thought of South Korea as more than a bunch of copycats. How will they remember their history in 200 years?)
Thirdly you're not acknowledging the fact that the USA historically had a deserved reputation for not respecting intellectual property. For example Charles Dickens had more than a few choice words about how freely his works were pirated verbatim in the USA. Key technologies were taken lock, stock and barrel without compensation - exactly what Americans today complain about Asian countries doing.
In short there are good parallels between how the USA behaved and was seen 200 years ago, and what's going on today in Asia.