I agree with your overall analysis, just wanted to note a few points where my opinion differs.
China's Army is now fully motorized (as in all equipped with vehicles) but not mechanized (as in all equipped with armored vehicles). The level of armor protection in the majority of Chinese armored vehicles is questionable and it seems unlikely that body armor is widely available to its troops.
China's Air Force is only partially modernized through the deployment of advanced multirole fighters. Bombers, transports (as well as all sorts of specialized planes based off of transports), and helicopters of all types are still lacking in quality and quantity.
With the rapid production and deployment of the Type 056 China's Navy is being thoroughly modernized in quality with modern types across the force, but is still in the process of building up enough quantity of existing types and introducing some new types (such as CVs, LPDs, LHDs) to meet the organic growth in the country's needs for a blue water force.
Despite all the equipment modernization and media coverage of exercises it is unclear to what degree personnel, tactics, and strategy have been adjusted to make full use of the modernized equipment. It is also noteworthy that China's military has not seen combat for decades and has never seen combined arms combat.
In a self-improvement context China's military has dramatically improved capabilities, this is also true relative to its weakest potential adversaries. However when compared to its strongest potential adversaries who have continued their own military advancement, China has merely kept up with having military capabilities that are barely sufficient to deter aggression and some coercion.
in a purely material sense you are perhaps correct, but i cannot agree with your analysis of the implications of china's military modernization. in the world of international military affairs, it is more about what you have and what people think you can do, rather than what you actually would and could do. china's biggest deterrant to agression were already created in the 1960s when they built the atomic bomb. delivery systems and potential consequences aside, everybody suddenly had to take china seriously in a way they didn't have to before. in the volitile world of cold-war superfactions, disagreements with potential adversaries like the soviets and the u.s. could very well spell atomic war (or the threat of atomic war), and china had to have something to bring parity to the table.
with nukes in the pocket, china didn't have to worry about much for a very long time. nobody was going to invade the most populous country in the world holding nukes, no matter how antiquated and ineffective their conventional troops were. because china did not have many relations with other countries, it did not have economic interests to protect overseas. when china began its economic boom with market reform, planners realized that soon china may become involved in disputes related to its economy, over influence, territory, sea lanes of communication, etc. that is when they began overhauling the conventional forces (the influx of cash and american support in the 1980s helped too) to deal with such a contingency.
china's military development has always been practical before anything else. it knows it does not yet have the ability to project hard power through a land/air war very far (technological bottlenecks like large transport aircraft/engine design, political obstacles like american hegemony) while it can muscle its way into getting what it wants through diplomatic solutions most of the time simply because of the size of its economy.
today, america rules the waves, and china has recently been trying to achieve naval technological parity with the west because the sea lanes of communication and trade are where its priorities are, so it can secure continued access over the raw materials that are the lifeblood of its economy. access and security of sea lanes are not something that any country will likely shoot off nukes over, but they are critical just the same, which is why china feels the need to expand the reach and capibility of its navy over the other branches of its armed services at this particular juncture.