It is, constitutionally, an enormous hot potato. MPs are elected by their constituents. Any body that can fire an MP is a threat to democracy. It’s easy to say that rapists should be kicked out. But sex crime is often a crime with no direct supporting evidence. False abuse claims are an overblown threat in the general population, IMO, but if “Parliament HR” was a real thing then there’s a very obvious and easy route to force out MPs who aren’t toeing the line.
It also has to be balanced against lawbreaking as legitimate protest. Imagine an MP rejected by their constituents to legalise cannabis. If that MP smoked a fat dooby in public it’d be entirely consistent with their political mandate, but they’d be at risk of most HR policies as well as possible arrest. That’s why the current process is that an MP had to be sentenced to now than a year in prison before a recall petition, they have to have done something really quite bad.
Or, put another way, if a Berlusconi type was elected tomorrow and everyone knew they were a gropey sex pest at point of election, what right would any political body have to deny the voters specifically what they have requested?
Morals shift over time, politicians often drive those shifts, there has to be space for politicians to shift those morals even if you don’t approve of them.
Having said all that I think the best answer is a more aggressive approach to recalling MPs, we should be able to hold our MPs to account more than once every five years if their electorate desires it. And we should also have proportional representation so that unpopular views don’t get into parliament because of First Past The Post split vote nonsense.