You're right, it was LKY's idea that some should have more children, others should have few or none. But he miscalculated one point, Muslims. His contraceptive, sterilisation and family planning campaigns couldn't work with them, even with a stick-and-carrot mix of incentivisation. No penalty or mandatory measures could be imposed on them. It'd be a worldwide Islamic conference issue if he dared to do it.
So the stop-at-two policy worked with the Chinese, especially with the high education high income families, to LKY's muffled horror. Population control policy completely missing the intended target.