The only problem with getting any particular person out of their job for being dodgy (as MP, or as Minister/whatever given that they're already an MP/Lord/other-higher-upperer) is that frequently their replacement, successor or even tansitional intermediary (while the whole role is abolished/subsumed/merged/re-split) seems to always end up at least as fallible.
Reporting bias, of course, as anyone perfectly and unimpeachably competent isn't going to have (true) reporting of their pre-emminent and proven suitability for the role. But all political roles do seem to end in failure.
Or quitting in response to someone else's failures (e.g. as Ethics Advisor). But whilst that would seem to make them honourable and suitable candidates to fulfill the role (assuming also no jumping well before anybody realises they could and should be pushed), they've just quit! Meaning anybody who has attained a given position is more likely than not a person who is not the most suited to the role, one say or another. An extension to the Peter Principle
That all said, even with the likely laser-guided attacks and counter-briefings from their natural enemies (including their own fellows, as well as those who are more party-politically opposed), even after much churning, the current cream of the Conservatives has been found to have a lot more of a sour taste than we should feel comfortable with. And no obvious quick-fix (or even medium-term one).