I doubt it, honestly.
Budgeting at an individual level is pretty different to budgeting for a business. And large businesses with indirect funding models, etc, is quite a different thing to a small business.
I could care less about their personal financial situation, but I would care about their experience in the sort of decision making they are going to need to perform. If someone had experience in these areas, and they've proven successful at these things, then I have no issue with their personal wealth. It's a non-factor.
However, to get experience in these things, they probably need to have been involved with decision making processes for larger businesses or government bodies.
(eg. I know smart and motivated people who work for water authorities in Australia. They're used to funding models, long term planning, what-if modelling, etc. They possibly aren't paid amazingly well, and would fit what you're calling 'middle-class' but they have relevant experience. Someone else might be nice, and have some broad ideas I like, but I'd be wary of voting unless they could explain in detail how the funding for such things would work, and what the real cost is, since I'd assume a level of naivete)
I'm using funding and budgeting as the examples here, but equally skills like being able to manage teams, provide governance and oversight to projects, and even just set up clear lines of communication and management all take time to develop.