23andMe don't do full sequencing, they just map small parts of DNA which are tied to features they test.

Right but full sequencing doesn't net you much with ancestry. Much more important is SNPs on a broad population.

Also, even if full sequencing were needed, we're not even talking de novo sequencing, full sequencing is routine daily work nowadays.

A few things off the top of my head:

1. collecting a DNA sample from a corpse is more difficult than having someone spit in a tube and drop it in the mail. It takes tools and a specialist

2. they want to compare with lots of different databases. Most GEDMatch data comes from genotyping arrays, that look at ~500k variants on the genome. However, different companies use different sets of single-nucleotide variants. Meanwhile, law enforcement databases look at microsatellites, which can't be assayed easily with an array. Sequencing someone to be able to use all the different databases would be on the order of a thousand dollars

3. The genetic testing companies do things in bulk. Your cousin's spit was run though the various steps (like PCR) with 100s of other samples. Doing it for a single sample is going to be more expensive

This is a fantastic answer, thank you.