I've heard the phrase "Generation IV" used about the Pebble-Bed nuclear reactors, which use graphite "pebbles" for moderating/cooling and are safer than present-day reactors because their "default" mode, given no power, is to shut down. But the Graphite, in order to be safe, has to be kept away from air. So these type wouldn't be safe in the (fairly common) combo of fire and breakage. But they do have the redeeming feature of being small, and more "fit-and-forget" than anything we've seen so far.
Perhaps if they could be installed deep underground, in the type of place in which nuclear waste might be buried, they'd be a goer? You wouldn't have to move anything at the end-of-life to make them safe: just bury them in situ.
Of course, you couldn't do this just any-old-where: you'd need safe geology, so the number of possible sites would be limited.
I can think of worse things for Mr Gates to spend his billions on than keeping a lot of physicists and engineers in theystyle to which we are accustomed