There are a lot of issues with PPP. The reason why it is used is because it is a way to get away from exchange rates. The problems with PPP is just as you wrote: it depends on how you measure the prices of items. And that varies greatly.
Also, even if a service costs 50% less in a poorer country than in a richer country, who says the actual service you get is equal in value?
The World Bank has another measurement, it's the so-called 'Atlas method' which smoothes out the exchange rate over a 3-year period. By that measure, China will (possibly) surpass the U.S. in the mid-2020s and perhaps never on a per-capita basis unless we see a total energy revolution(like fusion energy) and/or an extremely rapid production of electric vehicels. Not to mention issues like food, water and other resources that are already strained.