If Charles abdicates, his children receive the baton. But Harry's, and William's succession is under question with both being known not to have that much enthusiasm with the royal business.

If they too decline, line goes to their children below the age of majority, and the icky question of regency appears.

The regency in question notionally gives quite a lot of power, as the crown itself. If regency goes to the executive branch, it will throw out the last check on the Downing st. for may many thing, including the use of UK's nuclear weapons.