At the moment, with the current Conservative Party 'charade' at trying to elect a new leader the need for the 'People' to elect our PM could not be more obvious or needed.
Of all the elements from our six demands electing our PM would be really simple as at the time of a General Election, as well as voting for a party to govern, we would also be able to vote for the PM we wanted. This could lead to a PM who was from a different party to the one with a majority in the Commons but that doesn't stop the process of governance it just creates the need for policy compromises which is an important element of democracy. In America, for example, we have had a Democratic President with a Republican House of Representatives and their government still functioned.
An elected British PM's cabinet would also sit outside parliament, while approved by it, which would mean the whole Executive being held to account by the whole of Parliament.
Having an elected PM would dispense with the farce that we are currently experiencing as the Conservative party goes through the motions of a type of 'Buggins' turn' internal election for their next leader.