For instance, digging up a graveside and pulling all the artifacts out, without extensively documenting every inch of what was found at the graveside even uninteresting things like arranged rocks, destroys the context that might have yielded insights about burial customs.
Archeologists prefer everything to be left alone undisturbed, and generally the idea is you only go looking for artifacts when trying to answer a specific question, or if the site is going to be destroyed anyway for construction. From their perspective treasure hunters are going out there and destroying the record of history.
Consider: a painting restorer would be happy with a discovery of an old painting, and will eventually be scraping and polishing and removing layers from it to reveal the full picture hidden under the dirt and rot of the ages (carefully, a tiny bit at a time, after they've recorded what they're starting with, and recording everything as they go).
But if you just scrape random flakes of paint off yourself and send them over with no other information, they will be mostly sad and hardly happy at all. The paint is important! - without the paint, the painting is nothing; but the flakes of paint are not in themselves valuable.
A metal detectorists do not like unnecessary digging, so you can be sure that they will retrieve their objects of interest with the minimum upheaval necessary.
I liked your analogy very much!
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.