You only get ID'd for alcohol if you look like a kid. I haven't been carded in years. And when you do get carded, they look at your license, check the date, and hand it right back. No copies are saved to a database that could get leaked who-knows-where.
If a social media site is concerned that a user may be underage, I'm fine with them asking for some sort of verification. But a blanket request on everyone to ID themselves by default is just not the way.