From a political science point-of-view, a constitutional monarch may be view legitimately as exactly the same as a president in a so-called "parliamentary" system -- which is, of course, different than a president in "presidential" system.
In a parliamentary system, a monarch or a president are both mainly figureheads with (almost) no real power. To that limited extend it doesn't matter to a country whether they have a Monarchy or a President. However in the case of Britain and some other countries, history justifies a monarchy as it seems to me.
In one's mind, one ought to retain a separation between the Monarch as head-of-state and he/she as an individual. He/she may function perfectly well as the latter, while having minor flaws as an individual; more so for members of the Monarch's family.
It would be far more trouble than it's worth, IMHO, for Britain to attempt to transition from a Monarch to at President. Who might be President? Elton John maybe? Why not? Like I say, not worth the trouble.