I disagree.

Concretes succession

True to some extent, but hereditary monarchies are not immune from succession disputes which can lead to political instability. And there can be instances of dynasties dying off naturally without any remaining members or succession to incapacitated people, such as children or senile men.

somewhat apolitical figurehead

If they have any power, they will be inherently political and that will be known. The apolitical nature of monarchs only arose when constitutional monarchs appeared.

personification of the government

You can have this without a monarch, is Trump not the personification of his own government and the Trumpist movement?

Successors are already trained and guaranteed

This does not necessarily require the state be a monarchy. The Roman Republic had this, as do theocratic republics such as Iran and even socialist states.

Monarchy embodies lots of our values

I agree, although you do not necessarily need a monarchy either for this.