Based on my reading of some books from Lee Kuan Yew, the reason he did not allow total free media and speech was that he was very much concerned about the stability of the nation, and as such a small country, Singapore really can't afford any civil conflicts (it had suffered one before https://en.wikipedia.org/wiki/1969_race_riots_of_Singapore and recently https://en.wikipedia.org/wiki/2013_Little_India_riot)
Besides that, some of the "free speech" online are actually either falsified or in very explicit languages specifically targeted at raising culture hatred, and hatred towards foreign immigrants. They are not targeted at solving problems
Somehow, the reason that keeps people leaving Singapore is not the lack of free speech, but something else. Most of my foreign friends from University had left Singapore, either to US or China. For them, the biggest problem seems to be high living cost, no space for personal development and no job satisfaction. How to retain these talents may be a bigger issue here