A team has finished a game with 23-6 singles and extra-base hits 2 times since 1897, most recently Boston Braves on 20 September 1898. That is about one every 221,502 team-games.
Box score for the most recent one ↗
22-4 22-6 23-0 23-2 23-4 23-5 23-6 23-10 24-0 24-3 25-2 25-3 25-4
The whole distribution — Singles and Extra-Base Hits · All 18 shapes