We do not have a presidential system. We elect individual MPs, most with party affiliations. The party with the most MPs forms the government and who leads the party in Parliament is an issue for the MPs and members of that party.
Whether this is a good, bad or indifferent way of doing it is immaterial. The same rule applies to every party. Which ever party is in power chooses its leader anyway it chooses. It could choose its leader by height, weight, drinking capacity, drawing a name out of a hat. it doesn't really matter
Currently the Conservatives are in power, and how they choose their leader is a matter only for them. I fail to see that if Labour were in power things would be any different, the same applies even if the Lib Dems, Greens, or Monster Raving Loony got into power.
I am just concerned, that in a run of ballots where only MPs voted, the two to get to the public vote are just of such abysmal low quality with the gravitas, intellect and leadership skills of a turnip.
If you want the Prime Minister to be chosen by a national vote, then we need to have a Presidential system like they have in the US