That to me seems like the biggest problem with parliamentary systems (which have many other advantages, especially for new parties, local constituencies, etc.). Unless there's a sovereign, or some other system, it's often left up to the sitting government to decide when elections will be called.
That's not true for most parliamentary systems. In fact it's only customary in the UK to arbitrarily call elections when poll numbers are up. But even in the UK, there is obviously a maximum term between elections. And calling elections without reason isn't actually possible anymore. Theresa May had to jump through some hoops to almost lose her majority last summer.
In the US, a president who leaves office before the expiration of their term is replaced by the Vice President (or the next in the line of succession if there is no Vice President). In Germany, a chancellor can only recalled by electing a replacement. If they resign or die, the President gets to make a few decision, and they will usually task the leader of the largest party to find themselves a majority. Only after two or three failures of that process would a President turn to early elections.
