A team has finished a game with 21-7 singles and extra-base hits 3 times since 1897, most recently Minnesota Twins on 13 June 2017. That is about one every 147,668 team-games.
Box score for the most recent one ↗
21-1 21-2 21-3 21-4 21-5 21-6 21-7 21-8 21-9 21-10 22-0 22-1 22-3
The whole distribution — Singles and Extra-Base Hits · All 18 shapes