There has been some hesitation over the economics Nobel. Arindrajit Dube asks whether it is better thought of as a "Nobel for planning", and David Henderson says that we shouldn't be worrying about designing a market for kidney's - we should just "allow one".
I think these sorts of concerns are misplaced.
If you think economics is all about talking about the price mechanism and finding supply and demand equilibria, then you could see why this might be a concern. But that's not what econoimcs is about. Economics is about the choice and exchange behavior of humans that structure our use and allocation of resources (some people make a big deal about the difference between "choice" and "exchange", but I don't see much to that line of argument). Prices and markets, of course, are an incredibly important part of that. But economics isn't an apologia for the market. It's a science that studies the social behavior of one particular species of primate.
And those primates don't always use prices to allocate things. One reason why we don't always use prices to allocate things is that charging a price can actually change the subjective value of the good that we're talking about. Roth actually talked about this sort of thing in his paper on repugnance as a constraint on markets. We economists don't feel a repugnance for nearly as many things as other people do, but then again we also generally don't like to tell people what should be in their utility functions.
I don't think kidney markets are the best example to use, largely because I think the lack of a market in kidneys is largely due to an "initial yuck factor" and we'll probably eventually see a market.
A better example is the marriage "markets" that have also been getting a lot of press with this prize. In this society we marry for love (among other reasons), and the value of the marriage would be fundamentally different if we paid for it. That wasn't always true, and it may not be true in the future, but it's true for us now. Any scientist concerned with the allocation of companionship, time, sex, and pooling of resources in this particular species of primate has to get out of the habit of thinking about prices if they really want to understand the allocation of these resources.
Now you could be an advocate, and not a scientist, and say we should be able to pay for brides or grooms (as far as I know, though, your advocacy is complete - I don't think that's illegal). If you're a scientist you have to say "that's great, now let's try to understand how this group of primates actually does this".
This gets me to Dube's claim that this is a Nobel for planning. That's sort of true if by "planning" you just mean "non-price allocation". But it's critical to remember that Roth wasn't working at Gosplan. He was looking at the way the world actually worked with these non-price allocations, and then he tried to understand the implications of the mechanisms. General principles derived from those studies do have practical significance (as science often does), but he was studying existing human behavior.
If you really care about understanding how this species of primate allocates resources, you're going to have to accept a world where prices don't always exist, because I doubt that's going to change. We allocate within firms without prices. We bargain and allocate time and resources within families (something I'm writing about now for my Gender Economics class) without prices. None of this is going to change. And of course we allocate in government without prices, but that opens all kinds of philosophical discussions and once again leads people to put on their advocate hats and take off their science hats.