This should be tested
You should at the very least run a limited test of this feature in order to see how it goes and validate some of the assumptions that have been mentioned.
All of of the objections I've seen on this thread and elsewhere sound reasonable, but none of them are good enough to justify writing this feature off entirely without even testing it.
If it worked, it could be an amazing addition to SE, not to mention a minor source of revenue for SE and developers.
Objections
People who are desperate for money will abuse the system
Well, sure, people will try. The whole point of SE is that it's very good at detecting and preventing abuse.
The link juice and traffic that SE provides currently is already a massive incentive for abuse, and yet they're able to handle it very well.
The same could be said about point bounties - because they are an enhanced incentive they increase the potential for fraud.
People should answer questions because they're interested in the field not because they are offered money
People respond to incentives. If people are supposed to answer purely and only because of their interest, then why have points and badges in the first place?
Why not just post the question on another freelance project site?
You could say the same thing about SE's resume and job posting services. Why not just use existing services that are out there?
The answer is that SE has an amazing community behind it. The chances that my question will be answered quickly and accurately are simply much higher on SE than basically anywhere else.
Introducing a cash economy into a helping/gratitude economy is usually problematic:
http://freakonomics.com/2013/10/23/what-makes-people-do-what-they-do/
I don't see how this applies.
What happened in that study is that people basically expected more "service" once they started paying for it. Instead of picking up their kids 20 minutes late, they started picking them up an hour late because now they're paying for it.
I guess the analogy might be that askers would become more lazy with their questions when they were paying for them, because they assume they should get more "service" and not have to spend as much time preparing a well-framed question.
Sure, it's possible that money could decrease the quality of questions, but let's test it to find out.
Again the same could be said about point bounties. Because people are offering a bounty, they'll get lazy about their question and just assume it will be answered because of the bounty. But in fact it's usually the opposite - bountied questions have even more thought put into them, because the asker has more skin in the game.
Same would likely be true for paid bounties.
What if the person doesn't pay?
Seriously? Just do the same thing as what is done for point bounties! Make them pre-pay with no guarantee of getting an answer.
If money was offered, it would feel like work so I wouldn't want to do it in my free time any more.
I don't see why you'd feel less incentivized. Maybe slightly more incentivized but most likely you'd just feel the same. It's not like this would be your day job - who wouldn't want some extra pocket change for something they're already doing for free, particularly when they're creating value for someone else.
At any rate, the number of paid bounties is going to be very low. Kind of like how the occurrence of point bounties is quite rare compared to regular questions.
So the presence of paid bounties likely wouldn't impact 99% of what you're already doing on SE.
A Use case
Here's the use case that I have in mind. Someone has an urgent situation that they'd be willing to spend $100 or $200 to get resolved right away because it's important.
Sure they could find somebody on elance for that amount. But highly skilled developers aren't going to be available at a moment's notice off of elance, even if you paid market or above market rates.
SE is in a unique position to be able to connect the highly skilled developers who are available within minutes of the question being posted with the people asking the questions who need a quick answer.
And yes, SE already works extremely well to handle exactly this scenario, without any money exchanging hands - which is awesome.
But what if you have a particularly hairy issue and the only answers that you've gotten haven't been fully baked or require additional time to validate that you just don't have at the moment.
You'd be willing to pay $100 or $200 for a rock solid answer that just works. Someone who might normally spend 10 or 15 minutes answering the question now has a little more incentive to go ahead and spend the full 20 or 30 minutes to give that rock solid answer that's needed.
Sure there's the possibility that the developer spends the 30 minutes and then the asker says they didn't feel the quality of the answer was high enough, and so the developer is frustrated by that. But that's an existing problem on the site just with the point system.
People answer questions all the time and don't even get them marked as the answer or upvoted at all. There can be mechanisms to help with this such as the askers rate of marking a question as answered, etc.