I'm sure there's a lot wrong with Singapore but the closest countries with comparable quality of government are Australia and Taiwan or Japan.
If the Lee family have a cult of personality it's invisible to tourists too. And Cambridge didn't even put the thumb on the scales to let in the current generation of the royal family, you really think they care about the Lees?
Of course a top University in the UK cares about the Lees. If you were like Lee Hsien Loong and nearly guaranteed to be a next generation political leader, any sane self-interested educational institution would give you preference.
Universities do this all the time, accepting children of foreign oligarchs who have CVs and test results padded with dubious measures. Why do you think the LSE brushed under the table Saif Gaddafi's ghostwritten doctorate? (a) because they didn't notice, or (b) the network effect of having the presumed (at that time) next dictator of Libya?
Cambridge never needed to put the thumbs on the scale for the current generation of the UK Royal Family because they never applied.
Lee Hsien Loong's story just seems like a propaganda story tailored for the perfect Singaporean technocrat (clever, driven, and can fit himself into any institution). While he's no idiot, his life could have been dreamed up by the North Koreans, a meteoric career in the army, receiving the title 'Chief Wrangler' at Cambridge. It sounds like propaganda.
If the Lee family have a cult of personality it's invisible to tourists too. And Cambridge didn't even put the thumb on the scales to let in the current generation of the royal family, you really think they care about the Lees?