I think the issue is that politicians' reputation are so bad.
I think making rules based on people's dislikes is a bad idea.
And I think showing there is no conflict of interest is almost impossible.
I don't.
Even if you have a fairly draconian definition of a conflict of interest, it's better to make the rules on that basis than because people erroneously think all MPs are a bunch of scoundrels.
Anyway, it seems to me that being the editor of a high profile newspaper at the same time as being an active MP is a clear conflict of interest as well as being an impossible job - both are full time.