> If the crown was directly replaced with an elected president for instance, that would be an enormous amount of power for a populist leader to wield and the lack of policy responsibility would lead to populists leaders.

In practice, all of the powers of the Crown must be exercised, and must only be exercised, by the Monarch as directed by various configurations of notionally-subordinate officials (whether the Parliamentary majority or the Cabinet as executive committee of the Privy Council or...). Simply investing those powers formally in the institutions which direct them in practice would have no noticeable effect. Or investing them, with the same practical constraints, whether together or separately in, like, any random person chosen off the street. The advantage of a ceremonial Presidency in place of a monarch is that they could continue to do the ceremonial functions as well as signing where directed by the Cabinet, etc., without occupying the time of people with real and substantive responsibilities in government.