For a democratic nation our current process of selecting a new PM is abhorrent. To give the selection to a small number of paying party members hands them an exclusive privilege. It should be open to everyone in the country who is eligible to vote.
Can I suggest two viable alternatives. Members of Parliament are democratically elected (you may want to argue about how democratic our first past the post system is, but let’s stick with what we have for now). So as our elected representatives they could choose the next PM. Perhaps we could let them all have a vote, regardless of party.
Alternatively the vote could go to the country. Let everyone play a part rather than the paying few.
Either of my options may force the separation of the role of PM and party leader. Let each party elect its leader by whatever means suits them, but let’s be democratic in the selection of the PM.
I think either of these election processes would be infinitely fairer than what is happening at the moment, where the favoured few look likely to choose the most unlikely MP as PM on behalf of the rest of us.