At the outset of this multi-racial republic, when Yusof Ishak became the first president, it was already unwritten understanding that the presidency should rotate among the races. With Parliament nominated President, PAP or any party in power could do that smoothly. However, PAP had to be daft enough to make it Elected President. There's no hope of any non-Chinese winning if there's one or more Chinese contesting. What's the next best for a little pluralism variety? Peranakan of course.
Anyway, nominated or elected, the President is still largely ceremonial constitutionally. There's no power to make laws or policies. The difference of an EP is the power to veto reserve spending. However, Singapore is still a parliamentary democracy, not presidential (as in USA or Indonesia etc.) and Parliament will still have the final say with 2/3 majority. A 2/3 majority can do anything constitutionally including changing anything in the constitution.