A team has finished a game with 21-8 singles and extra-base hits 1 time since 1897, most recently Texas Rangers on 22 August 2007. That is about one every 443,004 team-games.
Box score for the most recent one ↗
21-2 21-3 21-4 21-5 21-6 21-7 21-8 21-9 21-10 22-0 22-1 22-3 22-4
The whole distribution — Singles and Extra-Base Hits · All 18 shapes