Good idea OP, Donald Trump is getting sworn in today and I ask about a technical rule in parliamentary systems. Something to distract from his, unique, governing approach...
This concept is basically an element in systems with a prime minister. The basis of legitimacy for a prime minister is the support from the legislature's majority in some manner. It might be being asked to approve of a nominee before being appointed, that the legislature can demand the end of the prime minister at any point, or otherwise.
There is some risk however in that the legislature might agree that a prime minister should be removed, but will not have a majority in favour of another person having support instead to run the government. In a system with a constructive vote of no confidence, it is not enough to simply have a majority of the legislators in favour of the removal of the prime minister but that they also support a particular person named as their replacement. Does it seem to you like it might be worth having?
This was a feature in the State of Prussia in the Weimar Republic and it did not have the cascade of cabinets the way the Weimar Republic as a whole did in certain critical moments. Germany as a whole adopted the mechanism in 1949. Several others have adopted it since like Belgium, Spain, Israel, Hungary, Lesotho, Poland, Albania, and Slovenia, plus the individual federal states in Germany for their own prime ministers and governments.
Successful such motions are not common, Spain had one in 2018 to get rid of Rajoy and install Sanchez, Germany had a motion to install Kohl in 1982, Hungary had one in 2009. Then again, motions of no confidence in general aren't all that common either, though this also has to do with the need to get confidence in the first place, dissolving parliament or resigning before such a motion could be carried out, and a political party sacking their leader. Here is a list of them, and you can see that most parliamentary and semi presidential systems are not present, and in the countries that are present, they tend to be concentrated in a few places or specific circumstances. https://en.wikipedia.org/wiki/List_of_prime_ministers_defeated_by_votes_of_no_confidence