I live in Lisbon where we have the same problem as lots of cities - cramming everyone into one square mile. Instead of waiting for some magical solution I wish we got to work building some more city to live in.
But the reason people want to be in the city, is what makes it a city: its density. Even if a city has equal density everywhere, the dynamic place where everyone actually goes becomes the place everyone wants to be near. So prices there will go through the roof if it can't be made more dense.
There are only two dynamic solutions to the circle of density creating demand for more density. They are best used together:
1) Continuous spacial density growth.
2) Continuous temporal density growth. Keep improving the speed and convenience of movement throughout the city.
There is no static, or fixed timescale, solution.
Also in the case of Tokyo, well its Japanese, the housing is tiny (relatively), and dense. There is also a culture of tear it down and build new, unlike the states. (Japanese housing is interesting in this regard, all value is in land not the home on it)
Shenzhen is just sprawling new construction. It will be interesting to see what that looks like in 10 or 50 years. I suspect much of it will be falling apart due low construction standards, low will to maintain standing structures, 100 year lease terms not actual ownership.
Us, Japan, China, and your country of Portugal are all facing declines in population (with the US propped up by immigration). Does building more make sense? Is the decline in construction a harbinger of what's to come? It's going to be an interesting few decades.
https://en.wikipedia.org/wiki/Boroughs_of_New_York_City
NYC is not "on an island" either.
I left Singapore in 2003 because it was getting ridiculously dense. Since then it's only gotten worse. The last time I went back it wasn't the city I knew but a doppelganger with a suspiciously main land Chinese accent.
Unless you want to have a livable city, and want nature nearby, yes sure, just grow, and grow, and grow. Btw, Shangaians f.e. want a word with you.
Perhaps Lisbon, as many other cities, should impose a limit on newcomers / population and area growth. It would help conditions and feel a lot.
In seriousness though, I do not believe we should shelter existing residents (read homeowners) from the economics they impose on newcomers. Removing tax breaks (Prop 13) would go a long way.