A team has finished a game with 24-3 singles and extra-base hits 2 times since 1897, most recently Boston Red Sox on 18 June 1953. That is about one every 221,502 team-games.
Box score for the most recent one ↗
23-2 23-4 23-5 23-6 23-10 24-0 24-3 25-2 25-3 25-4 26-4 26-5
The whole distribution — Singles and Extra-Base Hits · All 18 shapes