Actually, when I contemplate the Trump years in the USA, I feel more and more convinced that a system separating the role of head of state from that of head of government is a good thing. The monarch is an alternative source of (soft) power, being, psychologically, the focus of national unity and personal loyalty for the country (including the armed forces). This prevents all power being concentrated in one person. Because the monarch sits above party politics, he or she can unify the country in spite of the coming and going of the various political factions and heads of government, many of whom come to be despised by a large proportion of the citizens.
The monarch effectively prevents the head of government from getting too big for his or her boots, by acting as a reminder to the people of the limitations of the office of prime minister. There are quite a few monarchies in Europe (Norway, Sweden, Denmark, Spain, Netherlands, Belgium). Quite a few republics have chosen to split the head of state from head of government, too, e.g. Ireland, Germany, Italy, Israel. In Spain, the monarch even stopped a military coup, single-handed!
Don't knock it too much, when your own system is falling apart due to the overweening power of the president.