Yes, I think they should, for a number of reasons
1) It makes it easier to return to previous professions when they lose their seats. Who is going to employ a consultant surgeon who hasn't been near a hospital for 10 years or a teacher who hasn't been near a classroom?
2) It keeps them in contact with ordinary working people at all levels, whether in manufacturring, hospitality, academia or manu facturing.
However
I think there should be a limit to much time they can devote to this work - not more than 10 hours a week and their earnings from other work should not exceed how much they earn as an MP.
The danger if some MPs can not keep a side line going, to keep their professional skills up to date is that we will end up with more and more MPs whose whole life is politics from a very young age, they have no work experience, no professional training and no contact with us ordinary voters, our lives and our problems, can have no real understanding of the problems of their constituents.