A team has finished a game with 16-8 singles and extra-base hits 8 times since 1897, most recently Los Angeles Dodgers on 13 September 2014. That is about one every 55,375 team-games.
Box score for the most recent one ↗
16-2 16-3 16-4 16-5 16-6 16-7 16-8 16-9 16-10 16-11 16-12 17-0 17-1
The whole distribution — Singles and Extra-Base Hits · All 18 shapes