A team has finished a game with 25-4 singles and extra-base hits 1 time since 1897, most recently Oakland Athletics on 1 July 1979. That is about one every 443,004 team-games.
Box score for the most recent one ↗
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