I once had a similar thought, but I wanted to use periodic comets to study the solar system, not the comet itfself. Once they reach the outer solar system, comets lose their tails (become inactive) and would be great platforms for telescopes and other stuff. Depending on the specific comets orbit, they e.g. pass outer planets, the Kuiper belt, or even the Oort cloud. You wouldn't have to care for propulsion and stuff; you'd use some type of nuclear energy instead of solar panels, and you're good to go ;-)

That's basically rock bottom for western civilization...

It took the entirety of human history to develop all the techniques, instruments, harmonic theory, composition, organizing almost 100 people with different instruments to play together in an orchestra, training people to sing several octaves, and so on and so forth, and what do we do with that now? We consider it a useful tool to push away the homeless...