That way developers could pick the bugs where people are willing to put their money where their mouth is.
It seems that this might encourage developers to leave bugs outstanding or introduce new ones as a way to generate revenue though, unless a similar scheme is used to fund 'new features' and not just bugs.
Emphasizing this. This is why the police sometimes oppose safe streets and raised speed limits: it decreases their revenue from speeding tickets. It's a fairly well-known problem, though I've never heard of a fix.
For example, here's an issue with 11 backers: https://www.bountysource.com/#issues/27-split-pane-feature
...and here's a bounty over $1100 with 5 backers: https://www.bountysource.com/#issues/315019-add-a-tiling-win...
I think this is probably why gittip works so well. Set it and forget it.
Being a developer myself, when I create a piece of code to do a specific thing and release it to the public it's not for monetary gain, but to help others than need it by using my source. However, if they wanted additional features added to it, you could have a pot, and once the feature is achieved the pot would be deposited to the developer.