A team has finished a game with 17-6 singles and extra-base hits 25 times since 1897, most recently Los Angeles Dodgers on 18 September 2011. That is about one every 17,720 team-games.
Box score for the most recent one ↗
17-0 17-1 17-2 17-3 17-4 17-5 17-6 17-7 17-8 17-9 17-10 17-11 17-12
The whole distribution — Singles and Extra-Base Hits · All 18 shapes