I don't know, lab tests in a hospital go off to be analyzed somewhere. I think there's a healthy middle ground between "do it all yourself" and "let's store the results on a server connected to the internet indefinitely."
I agree that an affordable SNP chip you could use at home would be amazing though.
Or a kit that isn't attached to your real identity (fairly easy to do with 23andMe, they don't require ID verification).
If your family members attach theirs to their real identities, they might be able to figure out which one is yours.