A team has finished a game with 21-5 singles and extra-base hits 3 times since 1897, most recently St. Louis Cardinals on 22 August 2008. That is about one every 147,668 team-games.
Box score for the most recent one ↗
20-10 21-0 21-1 21-2 21-3 21-4 21-5 21-6 21-7 21-8 21-9 21-10 22-0
The whole distribution — Singles and Extra-Base Hits · All 18 shapes