A team has finished a game with 23-2 singles and extra-base hits 1 time since 1897, most recently Houston Astros on 30 May 1976. That is about one every 443,004 team-games.
Box score for the most recent one ↗
22-0 22-1 22-3 22-4 22-6 23-0 23-2 23-4 23-5 23-6 23-10 24-0 24-3
The whole distribution — Singles and Extra-Base Hits · All 18 shapes