I doubt that the change was mandated by the FCC. I wouldn't be a bit surprised if it started after somebody got robbed, and the networks (and everybody else that released addresses) realized that fewer people may enter because of it. Even with the TPIR (the Barker-era) Home Viewer Showcases, Bob would dial the winner's phone number, and if you tried hard enough, you could work out the number from the touch tones. (You can get around that now by "renting" 555 numbers, which can forward to other numbers - Vince McMahon did this for a WWE contest where he called people live - and which is the main reason all of the TV and movie 555 numbers are all now 555-19xx.
Then again, I remember when PBS local auctions would reveal the names and cities of winning bidders, then changed it to just the cities, then stopped doing that, so it's possible that there was some law involved, although this didn't start happening until sometime around 1980.