1) Build time machine 2) Greet time traveler who emerges from machine 3) Time passes 4) Time traveler enters time machine.
Lots of room for shenanigans, Fermi paradox solved.
Then it'd introduce a certain game-theory to it all: If you send something back in time, you're essentially losing it (or them) to a parallel universe, and turning on your receiver means accepting a gift from some possible future.
So some people will travel in time for their personal benefit (greeted as a celebrity with valuable skills and knowledge) and others will consider how to transmit all of their radioactive waste to another version of themselves...
Occam's Razor corollary #2: no one wants to visit this time period because, cosmically speaking, it sucks.