Those who could (spoke German or English, had degrees, had no prospects in Greece, had connections abroad, etc), that is, around 500000, have already immigrated in the last 10 years.
That would be like 16 million Americans leaving the US in a decade, including most 20-40 with a degree. That's on top of two millions or so that immigrated out of Greece in the 20th century.
Not everybody left, because there are benefits (cultural and otherwise, like the climate), that they don't want to miss, they have strong family ties (including a strong culture of taking care of their parents), they have houses and property here (and would have to start from nothing abroad, and they have no degrees. Last, but not least, the civil servants (close to 20% of the population with their nuclear families) still have jobs, while 2 million others (out of 10) are too old to go anywhere and start any career abroad (50+, pensioners, etc).
After the war the whole British Empire had the right to live and work in the UK - all 1bn of them. Even with adverts encouraging them to come they only came in tens of thousands a year. The economic differential was even higher then. I think the French Empire gave the right of residence in France around WW1.
The significant mass migrations have come from wars and disasters. Such as Syria most recently. Economic migrations have always been far lower.
Other countries would be "well within the scope" to manage 70m Chinese coming in in a decade?
(Other countries being the 5-10 more preferable immigration destinations -- the US, UK, France, Germany and co -- it's not like the Chinese will go en masse to Chile or Romania).
Even with open borders Chinese would not migrate at that rate when they are in a very different economic state to Greece. China is a place to migrate to rather than from as it grows in world status. It's inconceivable they would leave at that rate without first being a basket case (difficult without a Euro-comparable situation), or war and the traditional causes of significant migration.
Has EU freedom of movement resulted in dissolution of sovereign states? Did the absolute and total freedom to migrate by the two major empires result in the dissolution of UK and France?
With the free market in the EU why has the whole population of Greece not yet moved to Germany or France for the opportunity? Even with freedom of movement many won't want to, or have financial and family ties. The biggest surge came when the poorer Eastern European nations joined the EU and we had noticeable Polish and other communities forming - but were far from being swamped. The UK didn't become less the UK because of it. London, Manchester, Liverpool and the other major cities have had big immigrant communities since the early 1800's, long before passports and border controls. Border controls only really started in WW1.
America is more interesting. It was built on immigration and looks back to origins far more than many other nation's immigrants do - as seen by so many self identifying as Italian American, Irish American etc, and visiting their roots in Europe or wherever. With that identity so commonly given, it _is_ a big part of the culture already. That melting pot became America. It is America.
Why did it stop being a source of pride and development and become something to discourage? They don't lack space or opportunity.