The reason is very simple - there are more poor people than rich people. In a one man one vote society, the politicians will go for the poor to win more votes. The notion of "there is no free lunch" is only selectively applied - ask LKY why the people should vote for him - because he give out "free lunches" in different forms - eg HDB subsidies, GST rebates, Good Progress Report, free school books, etc.
If the "poor" were given more money, the middle class, most from which most of the 66.6% are formed, will be taxed more. That is why a "no free lunch, middle class pay less taxes" regime works so well in Singapore, because the 66.6% understand that. They also understand that a reCHEEme will ultimately tax them more, not less, so it is cheap to pay each minister $0.50 to $1 a year to prevent that because Singapore will be doomed without its low tax regime.