A team has finished a game with 22-0 singles and extra-base hits 5 times since 1897, most recently Los Angeles Dodgers on 3 June 1988. That is about one every 88,600 team-games.
Box score for the most recent one ↗
21-5 21-6 21-7 21-8 21-9 21-10 22-0 22-1 22-3 22-4 22-6 23-0 23-2
The whole distribution — Singles and Extra-Base Hits · All 18 shapes