A team has finished a game with 16-1 singles and extra-base hits 148 times since 1897, most recently Miami Marlins on 12 September 2016. That is about one every 2,993 team-games.
Box score for the most recent one ↗
15-9 15-10 15-11 15-12 15-13 16-0 16-1 16-2 16-3 16-4 16-5 16-6 16-7
The whole distribution — Singles and Extra-Base Hits · All 18 shapes