Deleting (destroying) everything after all tests have been done would be the simple solution.

No such thing. Any data that can be saved, will be saved. Deletion is a myth.

Well yes, because there are no laws and punishments which would disincentivize it.

What's the public health benefit to keeping blood samples around for so many years?

There are diseases (particularly cancer) that can be detected before symptoms arise based on the changes in the methylation of the DNA present in cells in the plasma.

To detect these, you need to have a baseline - the longer the better.

For one such study, The Project Baseline Health Study: a step towards a broader mission to map human health --- https://www.nature.com/articles/s41746-020-0290-y

> Further, while some participants’ samples have been assayed with a broad array of tests (Tables 2–4), participant samples will be stored for in depth testing at a later time when current assays are pertinent or new assays are available or new understanding of a disease process make performing a standard assay, not originally done, to be done on all or a sub-group of participants because of this new knowledge.

Research is the big/obvious one.