A team has finished a game with 23-4 singles and extra-base hits 2 times since 1897, most recently Boston Red Sox on 28 May 2005. That is about one every 221,502 team-games.
Box score for the most recent one ↗
22-1 22-3 22-4 22-6 23-0 23-2 23-4 23-5 23-6 23-10 24-0 24-3 25-2
The whole distribution — Singles and Extra-Base Hits · All 18 shapes