A team has finished a game with 17-3 singles and extra-base hits 81 times since 1897, most recently Chicago Cubs on 18 July 2023. That is about one every 5,469 team-games.
Box score for the most recent one ↗
16-10 16-11 16-12 17-0 17-1 17-2 17-3 17-4 17-5 17-6 17-7 17-8 17-9
The whole distribution — Singles and Extra-Base Hits · All 18 shapes