A team has finished a game with 19-7 singles and extra-base hits 6 times since 1897, most recently Kansas City Royals on 9 September 2004. That is about one every 73,834 team-games.
Box score for the most recent one ↗
19-1 19-2 19-3 19-4 19-5 19-6 19-7 19-8 19-9 19-10 19-11 20-0 20-1
The whole distribution — Singles and Extra-Base Hits · All 18 shapes