Singapore's success doesn't come from quality education for it's best students. Singapore's success happens because during colonial times the British nicked it off the natives and used it as a naval base. Because it's located on a strait that a large volume of traffic goes through, it became a major trade hub. This gave Singapore a bunch of cash cow industries that require a bit of capital investment (such as building massive oil storage facilities) but dont require much else. With that money, Singapore can afford to import whatever it wants, such as foreign doctors to take care of it's population. In many regards it's similar to an oil rich country like the UAE.
It was not the only port located near the straits of Malacca and nor was it the first or biggest. Even today Malaysia, Indonesia and the Philippines have more oil and the same traffic (with Malaysia even having multiple of the world's busiest ports) but not the same wealth. Singapore was given no cashcow industries like rubber or oil and when it was kicked out of Malaya it had no resources, no industry, was dealing with the aftershocks of race riots, commies and Japanese bombing - it was a third world country with access to little capital and not much else. The reason why Singapore has ludicrous amounts of money now was because they invested it well and attracted even more investment from Americans and Chinese, convincing them that it was worth their time; building up manufacturing industries, investing heavily in education and ridding corruption (alongside dissidence) to make Singapore stand out as a safe investment area. Its success was not inevitable, its success was promoted.
It didn't go from this:
To this:
Without the smart sweaty brows of Singaporeans, you don't become a major financial hub for nothing.
Also give the colonial Brits some credit; it wasn't used as a naval base until WWII, before then it was just a trading post - and it had competition from the Chinese, Portuguese, Spanish and Dutch. And it won, by essentially doing nothing because no one likes paying tariffs.
*EDIT
I was wrong, the Singaporeans invest even
more in education than I thought.