A team has finished a game with 16-12 singles and extra-base hits 1 time since 1897, most recently Boston Red Sox on 27 June 2003. That is about one every 443,004 team-games.
Box score for the most recent one ↗
16-6 16-7 16-8 16-9 16-10 16-11 16-12 17-0 17-1 17-2 17-3 17-4 17-5
The whole distribution — Singles and Extra-Base Hits · All 18 shapes