If you have two countries with equal GDP in PPP terms, but one has double GDP in nominal terms because local prices are twice as high, their economies are not equal. The country with higher nominal GDP has much more purchasing power for imports of raw materials, technology, weapons, etc., or to make investments.
It depends. There are a lot of issues with nominal GDP (converted to USD directly) as well.
It assumes USD based trade/capital flows are
a) something like 20% of total GDP to achieve something close to pareto quantitatively
b) the impact even if a) is met is pareto qualitatively on the remaining 80%
Most times a) isnt met to begin with and b) is of varying correlation to extrapolate 1:1 to from that 20% (i.e final consumption and final investment rarely sufficiently mirrors what is traded/intersected with others)
That was the whole reason why the concept of PPP started since large countries at the time (1980s) such as PRC were barely having any trade intersection with the world to begin with, yet obviously were consuming energy and other base inputs far more than the resulting nominal conversion suggested.
There is nothing intrinsically wrong with China having a higher PPP GDP than the US today. It has advanced considerably post-Mao and has a population 4 - 5 times higher than the US. It is simply matter of time it consumes more than the US does. Same goes for India whenever that happens....again the population is much higher than the US.
It is not PPP's fault either that the GDP nominal is inflated with various countries. All PPP does is more accurately reflect the 80% bulk of economy that is not following the pareto correlation transmission by looking at actual prices and consumption scales there. Part of reason CCP has also not allowed same sampling rate (number of cities allowed in survey etc) like other peer countries do if you look at the relevant papers involved.
i.e that is separate matter with say PRC and it being brought up like it did with Wen Jiabao and Li Keiqiang, the reforms they suggested (at local CCP level where there was bad incentive structure in reporting and tabulation and errors compounded over time to make it "unreliable") and so on..... till both them and their factions were suppressed by the current guy. Those that also use (or are convinced by) the nominal figure in "beijing CCP asserts so" weathervane kind of way with no proper caveats added. given all this....again thats on them.