.....so why not for a Prime Minister?
Because it would compromise a basic democratic principle. It's up to each political party to elect/select its leader in its own way. It's not comparable with selecting people for senior management jobs in a commercial context.
To my way of thinking A potentially unfortunate outcome in our political system is that we can end up with having new party leaders (and therefore Prime Ministers) in mid term. Let's hope we get someone who can do the job that has to be done.
I share your concern about the apparent lack of neutrality on the part of some civil servants - they should not be publicly voicing their thoughts in this way.