This has the problem of being near worthless until you have both a large pool of experts and a large pool of paying customers who want that expertise. It's got pretty much all of the problems of the question/answer sites (which StackOverflow seems to have proved convincingly can work, though it's pretty rare that it does), and few of the benefits to you the developer (the benefits you lose include all of the viral elements, all of the SEO, and anything else that comes from having a huge bunch of useful user-generated content that is publicly accessible).

That's not to say it can't work...I just don't have any good advice to offer on avoiding being a dead zone that attracts no search traffic, has little incentive for people to signup until a bunch of others have already done so, etc.

Now as far as this particular idea on selling experience, I would imagine the traffic and activity would start from the ones interested in selling the experience. The interests need to start with people with valuable experiences who may show interest in trying out the service to see just how profitable they could be by sharing their unique experience. Then this can spark interest in the "buyers" who may find the right experience/knowledge they were looking for.

If you get the right distribution, I believe it can overcome the challenge you speak of. The question I would ask you is: "If Google launched this service tomorrow, would you think they can make it successful?"

This said, I would agree that it would be a challenging start-up if you do not have the right plans/capability to scale up.

This is why I explicitly brought up answer sites. Your idea doesn't get the benefits of those kinds of sites, because publishing the expertise limits your ability to sell it (and makes it into another answers site). If you don't publish it the site does not become incrementally more valuable every time a question is answered, as Stack Overflow or Yahoo Answers does. It always remains a place where someone can buy expertise from someone they don't know, with qualifications that may or may not be accurate, for a price that cannot be compared.

My point is that your proposal seems like it would have all of the negatives of starting a new answers site, but none of the long term benefits. Answers sites start off with these problems, but may eventually overcome them as more and more questions get answered and the pool of regular readers and submitters grows, but yours would have these problems forever. Your site doesn't get bigger, stickier, and more powerful, when you sign on new users and new experts.

I'm not saying you can't do it, or that it won't be successful. I don't know. As Paul Buccheit says:

Limited Life Experience + Overgeneralization = Advice

I simply don't see how you (or even Google, who have retired their own Google Answers) could overcome those barriers and reach a self-sustaining business.

As someone that connects industry specific knowledge to people that need knowledge, and perhaps has tools that make that task easier, you could very well have a lucrative consulting gig. But, I don't know that you'd have a startup.

But, what do I know? I build systems management software.

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So besides the critical mass issues raised by other commenters, your information providers would have to be either cheaper, more experienced (neither realistic), or somehow provide a far richer experience than these two well-regarded examples. That's a big hurdle & it doesn't scale well.

A lot of them are not really what you're talking about, but some are. "I am a Tax Researcher: Ask me anything" and the like.