A team has finished a game with 16-6 singles and extra-base hits 57 times since 1897, most recently Colorado Rockies on 9 August 2022. That is about one every 7,772 team-games.
Box score for the most recent one ↗
16-0 16-1 16-2 16-3 16-4 16-5 16-6 16-7 16-8 16-9 16-10 16-11 16-12
The whole distribution — Singles and Extra-Base Hits · All 18 shapes