First, it seems to me that monarchs have more invested in the legitimacy of monarchy than ministers have in the legitimacy of democracy. Second, an elected official may be expected to sacrifice themselves for the good of the population, whereas the roles may be reversed for a monarch. Third, succession works differently in democracies than monarchies, which may make assassination more attractive against elected officials.
First, it seems to me that monarchs have more invested in the legitimacy of monarchy than ministers have in the legitimacy of democracy. Second, an elected official may be expected to sacrifice themselves for the good of the population, whereas the roles may be reversed for a monarch. Third, succession works differently in democracies than monarchies, which may make assassination more attractive against elected officials.