I can see how this might seem like an obvious solution at first glance, but all it would do is make the problem of amateurs destroying the context of finds worse, and by a lot. This kind of incentive will provide for many artifacts and little knowledge, as most artifacts are useless without the context in which they were found.

It is of course appealing if you think that all an artifact is good for is looking nice in a glass case. But if you want to gain knowledge about the past, this would certainly be the worst policy you could implement (apart from obviously insane ones, such as a bounty for destroying artifacts on sight, of course).

But I already wrote an extensive rant about this in another comment, which you might find interesting if you are curious about the topic. If so, sorry about the bad writing style and potentially divisive rhetoric, I'm supposed to be working decided to take a quick peek at hn where I found some discussion about a pet peeve of mine, which is of course a recipe for disaster.