There are different kinds of president. The President of the US or the President of France have a lot of political power. The presidents of Eire, or Germany, less so. But they have a role in the constitution. Heads of state have a responsibility in the constitution of a country, and its something we're not currently getting from the people who ride in carriages and wear jewelled hats.
If we want joy and pageantry, that's one thing. But it doesn't really help our country other than as a distraction from the fuel bills and the corrupt government. But if we want a modern democracy, that's quite another thing. I have to say I am dreading all the "celebrations" that we are going to have in a couple of months, while the people of this country are mired in a cost of living crisis worse than many of us can remember.