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...it costs even more money. With execution, your suggested recommendation, you still have to dispose of the bodies.

There's a free-market solution, and it's actually quite simple: privatize all land in the United States. The land-owner has the right to shoot trespassers. After that, whose property is the body? Obviously, the original owner no longer can claim it; therefore unless a will clearly bequeathes it to somebody, it is abandoned property.

The land-owner has first dibs, since its on his land, and can do what he wants with it. Presumably, a market for these raw materials will exist; perhaps a fertilizer or animal-feed company. Soylent green, maybe. Instead of a state-centric disposal problem, we have a free-market solution that produces benefits and generates wealth.

the cheapest solution is repatriation

Don't forget the need for a deterrent. Repatriation after public flogging, maybe. Sure, that's fine with me as well.