A team has finished a game with 20-7 singles and extra-base hits 3 times since 1897, most recently Boston Red Sox on 5 August 1979. That is about one every 147,668 team-games.
Box score for the most recent one ↗
20-1 20-2 20-3 20-4 20-5 20-6 20-7 20-8 20-9 20-10 21-0 21-1 21-2
The whole distribution — Singles and Extra-Base Hits · All 18 shapes