
The basic notion of representative democracy in its various forms is that the popular will of the citizenry is translated into government that serves for a time and attempts to govern in a way that comports with the will of the voters who elected it. There are various ways to construct such a system, with the two major types being presidentialism and parliamentarism.*
A basic model of democracy, as I have shared before, looks like this:**

The key issue here is that the power to govern comes from voters. But, of course, the simplified model is not what tends to exist in reality, although it is pretty close to what a unicameral parliamentary system would look like. That is: the voters choose the parliament and parliament chooses the government (PM and cabinet).
In parliamentary systems the voters delegate to the legislature only. In presidential systems they delegate to the president and to the legislature.

Of course, either model can be further complicated if there is an elected second chamber and/or if there is are elected sub-unit (e.g., state) level.
Of the various implications of the dividing of governmental power into discrete elected units is the question of who is really responsible for both successes and failures of governing in a given period of time. In parliamentary systems the issue of responsibility is clearer, given that the majority party (or coalition of parties) is clearly the course of both legislative and executive decisions.
Note that in the parliamentary model, the power to select the government (the PM and cabinet) is given to the parliament by the voters. (This is the basis of my previous post on the UK situation). And, ultimately, parliamentary democracy focuses more on parties than on persons (although, certainly, individual leaders are important and can very much matter politically and electorally).
But, as with the Boris Johnson issue, the voters in a parliamentary system empower parties to govern, not individuals. The parties choose individuals (the Prime Minister, but also the other Ministers of government) to exercise that power.
One can argue the virtues or vices of separate elections for executive and legislature, but it should be quite clear that the democratic accountability exists in both systems, and I would argue is actually more acute in the parliamentary system given that the voters know full well whom to blame or give credit to.
To further map these ideas out, here is a model for a parliamentary system with multiple parties:

Note that the voter vote for parties and then the parties that are able to work together to control a majority of seats are given the responsibility of forming the government. Again: a parliamentary system empowers parties to govern, not specific people.
And here is a model of the US system under the 1789 constitution before popular election of Senators:***

This is a more complicated model that split citizen input into multiple pieces. On the one hand, citizens are able to have an input on the House, Senate, and Electoral College,**** but that also means that each component can blame the other/take credit.
*There are other various including semi-presidential systems like France which have both an elected president and prime minister. There are also variations linked to how many chambers in the legislature (and what powers those chambers have), federalism, and a host of others. See Taylor, Steven L., Matthew S. Shugart, Arend Lijphart, and Bernard Grofman. 2014. A Different Democracy: American Government in a 31-Country Perspective. New Haven: Yale University Press.
**Fig 1.1 from Taylor, et al., 10; Fig 2.5, 56; Fig 8.2, 232; Fig 8.3, 240
***I need to make one that reflects the changes the system has undertaken, but not today.
***The electors were chosen by a variety of methods early on, with the popular vote becoming the norm around the middle of the 19th Century.









