Comment by Tuna-Fish

DNA in the ground has a half-life of ~500 years. After 2000 years, ~6% of the DNA remains. More crucially, there will not be a single complete chromosome left, it's all a jumbled, mixed mess of DNA fragments.

This can be reconstructed, but it requires a much larger sample than normal DNA analysis. (You need to get enough fragments to get a whole genome, with enough overlap everywhere that you can reassemble the pieces.)

The largest problem after that is that the vast majority of DNA in all your samples will not be human DNA, but DNA of the various bacteria that live in the soil. This doesn't ruin the sample, because you can just reconstruct everything and then discard all the things that are not human chromosomes or mitochondrial DNA, but it does greatly increase the workload when compared to a pure human DNA sample.

There are a lot of smaller problems that I am eliding here. But amazingly, all the problems are solvable, and the progress in this field in just the past decade is staggering. We have usable fragments that teach us new things that are >500kyr old, the oldest complete human genome we now have is ~45kyr old, and more recent samples are solving hundred-years-old historical debates, and new ones are done almost daily. We are living in the golden age of archaeogenetics, and many papers published today on it will be cited for a hundred years or more.

... but all the solutions to those problems create a lot more work, and thus a lot more cost than those $500 gene sequencing kits.