A team has finished a game with 14-7 singles and extra-base hits 73 times since 1897, most recently Texas Rangers on 16 May 2019. That is about one every 6,068 team-games.
Box score for the most recent one ↗
14-1 14-2 14-3 14-4 14-5 14-6 14-7 14-8 14-9 14-10 14-11 14-12 14-13
The whole distribution — Singles and Extra-Base Hits · All 18 shapes