Why do some Parliamentary Republics have a ceremonial president who isn't even voted on by the public?

Germany, Italy, and India are all examples. Their job is to serve as a ceremonial figurehead, kinda like a monarch in Europe today, but they don't work as that because they're nowhere near as globally well-known as, say, the King of England. If you asked me to name the Indian head of state, I would confidently say Nahrenda Modi, and I'd be wrong. The real "head of state" that no one has ever heard of is their president. I can't even tell you the presidents of Germany, Italy, and India, even though I could name Friedrich Merz, Giorgio Meloni, and Nahrenda Modi. And it's not like these are well-respected and universally beloved heroes being appointed. More often than not, they're just politicians. Politicians are literally the most divisive people in any country.

Another thing, these guys aren't even democratically elected in the same way other presidents are. In Germany, the president is appointed by an assembled electoral college made up of various politicians. In Italy, the President is appointed by the legislature, and in India, which probably has the strangest system of them all, only allows people who hold public office to vote in presidential elections.

Most of these were created to replace the role of a constitutional monarch, but is there even any solid reason to have them appointed instead of elected?