Consider the bounty as payment for giving the question more attention. When you drive a car, you don't get the fuel back, right? Yet energy is conserved--converted into a different form. Here, the "energy" (rep) is converted into a "different form" (attention).
The intended functionality of a bounty is to give the question extra attention (also to entice users to take extra time and write more detailed answers). You pay for the attention with the rep--you can't recover it if it doesn't pay off. Touching on cars again, you don't get the fuel back if you took the wrong road and got lost (thus wasting fuel with no gain from it).
Stealing @Dave's analogy (unfortunately not energy-related) from the comments:
My company can pay money to put a sign on a billboard. Will people read it? I don't know. Will it get people interested in the business? I don't know. Will I profit from it? I don't know. Will it be displayed in the billboard? Yes! Because that's what I paid for.
Another issue with refunding bounties is this:

Lots of people will just never revoke the bounty (i.e., keep re-applying it), and the featured tab will get cluttered. Eventually, it will become like the Unanswered tab--full of lots of questions of which a small percentage get answered. The only difference is that there's an extra rep gain, so people will like using this "new unanswered tab" better.
Currently, there are few enough bounty questions tagged javascript (for example) that I can look through the list, and decide which I'd like to solve (in my case, the ones with few answers, not using arcane frameworks, and within my level of expertise). If there were a few hundred bountied JS questions, I'd never be able to go through all these. This is what you lose when you flood the bounty tab.
So, placing a bounty will make it get lost within the featured tab. Of course, you could sort the tab by "newest"--but that's extremely unfair to users who use bounties to get attention/answers for their old, unanswered posts (one of the primary uses for bounties, in fact). If they sort it by posts that have recently been bountied, the re-bountied posts will come up. Yes, you can come up with a "been bountied only once/etc" metric, but that just gets complicated.
Also note that there already is something to make re-bountying harder (the re-bounty must be higher than the previous one). Now, there's probably a reason for it-- if the post didn't get an answer, it's probably not worth the previous bounty . This feature request works against the spirit of the existing feature.