Noah Smith likes to point out that if China's rapid growth starts petering out right when its nominal GDP is on par with the USA's, that's actually a pretty terrible outcome and in line with the middle income trap (after all, there's four Chinese people to every one American, so if US and China are at parity in 2030, Chinese GDP per capita will still be 1/4th of the US). China wants to be at least 50% larger than the US economy before its rapid growth stops, and doesn't look likely to get there.
Then again, we are talking nominally. Wouldn't standard of living more coincide with what is being generated on a PPP basis? For example, when I was working with the outsources, most of my coworkers were living in either Hyderabad or Chennai. One of them at my experience level was making about "a lakh a month", or about 15k a year. However, rent was 200 a month and food and medicine was about a quarter of the cost it is here. Tylenol here is 6 dollars. There, the same bottle is 100 rupees.