"It depends".
There is a very profitable cottage industry in certain African countries based around extracting stuff from the hard drives of old computers. I don't know how much effort they put in before they get something useful, but I've seen the film.
If I give away an old PC, it goes without a hard drive. The hard drive either goes into one of my existing machines, or a caddy, or is treated to some sledgehammer reformatting before being buried in the garden.
My daughter had my last laptop. I bought a used hard drive for £20 and installed that, plus all the software. The original hard drive is now pushing up daisies.