I don’t really understand why we would need to replace the monarchy with a President or similar, if we got rid of them.
I know in theory the monarch acts as a sort of “last resort” check and balance on the government. But frankly it’s been clear for a long time that the monarch won’t intervene. Remember Boris’s completely illegal proroguing of Parliament to avoid discussion of Brexit plans? The Queen went along with that despite it being unlawful.
The supposed “check and balance” from the monarch doesn’t exist. They know their own position is too precarious and relies on being non political.