A team has finished a game with 22-1 singles and extra-base hits 1 time since 1897, most recently Chicago Cubs on 6 July 1920. That is about one every 443,004 team-games.
Box score for the most recent one ↗
21-6 21-7 21-8 21-9 21-10 22-0 22-1 22-3 22-4 22-6 23-0 23-2 23-4
The whole distribution — Singles and Extra-Base Hits · All 18 shapes