I've now looked at the snap counts of every team in 2020, and can conclude that only two teams had fewer than 3 players who were Special Teams Only position players. I defined that as players who had significant ST playing time (150+ snaps) but whose median snap count in his nominal position was 3 or less. The two teams were GB and NYJ. 11 had 3 ST only players. The rest had 4 or more, up to 7 for Denver. NE had 4 last year.
My spreadsheet:
This whole discussion is based on false assumptions, that Belichick is some outlier. He is not.
13% of 53 = 7, so besides the P and K, you'd expect about 5 players whose primary value is ST.