No, it's a waste of bandwidth and time in this case as there's a simple 5 second solution. It reminds me of the Windows re-install Win98 over top of itself all the time crap. This is UNIX. There are nearly always better solutions than start from scratch.
After running into this twice now, the only thing one needs to do is go to http://www.java.com/en/download/testjava.jsp and it will say "disabled plugin" where the Java test should show up in Safari. Clicking in preferences to disable and reenable Java, for example won't do a thing to enable it (although it does have to be "on" there regardless). Clicking on the words disabled plugin on that web page will make it work again. Simple problem solved with a simple 5 second solution.
The alternative here is potentially waiting an hour+ to download Mountain Lion again (which you cannot even do from the App store if you bought a new Mac with Mountain Lion already installed; the App store will not show it as purchased; you have to use the restore partition instead; I only have it purchased because I bought an upgrade later for my MBP; that one will allow it to be installed on any Mac). But WHY ON EARTH would you do that when it's just a disabled plugin??? It's like fixing a crack in a wall in a building by tearing the entire building down and re-building the entire thing rather than just fixing the crack. Even if that building can be rebuilt in an hour, I'd take a 5 second solution over that any day. This is a non-issue problem that has a simple solution and that is the ONLY solution that should be presented as brute force is just a waste of time and only further propagates operating system ignorance rather than finding the true cause of the problem (which is a small bug in Apple Safari's internal settings). Sure if that's the only tool in your toolbox and you have a problem it might fix it, but once a better solution has presented itself, that's the way to go.
Facetime resetting its password settings described above was probably due to an internal update of either it or keychain and it would do it again if I updated the whole thing from scratch. Once again, it doesn't call for starting over, just filling in the password again. The only thing that made it look weird is it was past that point when it started itself up. You have to click BACK to the previous page and enter the password and then forward. Otherwise, the "next" button won't do anything and it won't give any feedback as to why not. Once again, Apple has made a two-bit application with Facetime (other bugs include "sticking frames" with some web cameras, an inability to transmit many sounds other than voices over the Net like music which simply gets garbled or muted instead and no ability to do conference meetings, etc. I see no efforts on Apple's part to improve it either. They think it's good enough for iOS and the Mac version is just an apparent after-thought, it seems. There is no Windows or Linux version and so you're limited whom you can conference with anyway. Despite all Skype's problems, it's still the best choice between platforms and has none of those issues (although it does crash sometimes and uses a lot more CPU time for HD video).