Why not?
They will certainly have more knowledge of what the everyday person wants and needs than those in power currently.
Provided they have the mental aptitude then really, why not?
We currently have people in positions dictating to others how to act, how to work and how to live when they have no knowledge of that themselves.
Take the education secretary. She's a bloody lawyer. What the hell does a lawyer know about teaching?
This is the issue really with a lot of politics.
Everyone has an axe of some sort to grind. Teachers (naturally) want more money. Nurses want better hours and more money. Tube drivers want more money. I'd love to get full healthcare and not have to pay £200 a month for a private physio to sort out my tendonitis in my ankle. Everyone wants something, and there is (arguably) justification for most of these demands.
Unfortunately, there is simply not the money for everyone to get what they want. Often, there is not even the money for people to get some of what they want. Intelligent and reasonably impartial people have to make decisions about what is best for the country as a whole.
Yes, we could have checkout workers, nurses, firemen, bin men and tube drivers in Parliament, but you'd end up splitting parties and politics by profession.
I appreciate that there are arguments that currently politicians are lining their own pockets and those of their backers, but this is why left wing parties exist. If people earning a lower income dislike it, they have the opportunity to vote and drive their parties into power as a group, rather than dividing into factions.
I don't like the current political system at all, but it's incredibly hard to think of something significantly better.