My view as an American is the British monarchy's value it tied to its links to tradition and its role to remind people, they are British and what that means. Even as that definition of what it means to be "British" evolves.
As the demographics of the UK change and evolve, it becomes critical to create "one people" who share a common identity, out of this incredibly diverse mixture of races, religions, and cultures.
The first step may be something as simple as embracing British traditions, the monarchy being a visible sign of those traditions.
In that sense, the monarchy must be a unifying force in the midst of a divisive world where politicians use differences to separate people into identity groups and then cater to those groups to gain political power.
The challenge of being a unifying force makes the behaviors of the "royals" critical. Those who can't or don't want to carry the burden of that responsibility should be separated in some tangible way from "the monarchy". They remain part of the royal family, but not part of the "institution" defined as the monarchy.