in the mid 80s when LKY, then just over 60, was exploring his next step, the expectation at the time was he would move to the presidency – under the then constitution, parliament would appoint the president by a simple vote; he being who he was, the position would not be merely ceremonial but he probably felt not comfortable with a position that legally carried no power and was subject to cabinet/parliament decision; so a move was made to change the constitution and enhance the position; the public discussion led to his undertaking not to be the first elected president; Goh Chok Tong then closed the option of LKY being the second elected present, with a decision to invent the post of Senior Minister to keep LKY in the cabinet;
the subsequently elected president Ong Teng Chong found that the constitutionally prescribed new duties required certain information regarding government finances and asked for a complete set of data, which caused friction with cabinet and some civil servants. Further, the 2nd and 3rd presidential elections never took place, because there is a provision that a candidate must possess adequate administrative experience, the assessment being carried out by a committee of three senior civil servants; in effect, the 3-men committee “elected” President Nathan twice, by rejecting other candidates as not being sufficiently qualified.
if LKY had retired in 1990 and then started a newspaper column (modern idea would be blog) or a charity/research foundation, and he would have remained the most influential person in the country, taking into consideration that his son and his 2nd cousin (Tony Tan, currently the 4th President, elected in 2011 with with just slightly more votes than Tan Cheng Bok) were both in cabinet; if he had been a blogger posting articles daily, every important person in singapore, the cabinet ministers especially, would have eagerly read them as soon as they were posted.
Further, it would have been possible to make a different kind of constitutional change, by creating a senate with a proportionate electoral representation, e.g., if there are 20 members, a political party will send one senator for every 5% national vote it receives; this would have provided a good venue for retired ministers to stay around and have a voice on policy, without having to have power to pass or reject legislation, but merely being able to discuss and advise; by ensuring that small parties that cannot get any candidate elected in a first-past-the-post system, can nevertheless get some electoral representation, the system also makes the method of “unelected parliament members” unnecessary; undoubtedly, if LKY had stayed on as a senator instead of cabinet minister, he would have remained the strongest public voice in Singapore without exercising ministerial power nor receiving ministerial pay.