The founders intended for rights to be settled at the Federal level, at least for those they considered to be worth giving rights to when our founding documents were originally assembled. They were on the right path by setting certain things there and not openly ascribing the federal government power since, hell, they saw what Britain's gameplan was in addition to wanting to set a level playing field for every American. But as forward-thinking as they were, they couldn't foresee every possibility in the future.
Amendments had to be put in place to set forth rights at the federal level because states many wouldn't do so on their own. This (depending on the case) was either because those groups receiving the rights couldn't actually vote or weren't considered to be valuable enough to be given any rights, much less the right to vote, or their votes were minimized in power.
There's also a giant leap between granting medical privacy rights and the Soviet Union. In fact, providing privacy rights is something the Soviet Union (and right now, the Russian Federation, as Putin is borrowing heavily from the playbook he probably helped write) would actually frown upon.