Yes 12 ly is amazingly close!
> If we presume there's nothing special about our little corner of the universe, then the distance to the nearest potentially habitable planets gives us an estimate of how many habitable planets are out there
I would put a slight caveat to this - I would argue we do know there's something "special" about our little corner of the galaxy, at least - we are in the continuously habitable zone - for example, there are billions of stars at higher densities closer to the core whose planets are likely uninhabitable due to toxic levels of radiation, GRBs, etc. So I actually might expect other planets near us to be more habitable on average than at least some other places in our galaxy.
But I also think it's too soon to know how potentially habitable these planets are, until we have a chance to check a bunch of other things on the checklist, like the long-term stability of the sun's output and the planet's orbits, the frequency of destructive solar flares, the frequency of asteroid bombardments (if there are no Jupiters to absorb them), etc.
Regardless the close distance should make it much easier to answer these sorts of questions than it would be far planets much farther away, and I'm excited to see what we can learn in the coming years.