This makes certain sci-fi shows with entirely too many habitable worlds in one system sound a lot less silly, however contrived the 60 Earth solar system configuration may be. And in any case, it brings "all your eggs in one basket" to an entirely new level.
While it is tempting to imagine a species actively creating this setup by moving worlds, the simple fact is that if you can move dozens of planets to a single star, you really ought not need to.
But boy, think of how compact the Federation could be if all the member worlds (with room to spare) got packed into a triplet of this configuration . . .