I've come to believe that this widespread belief that Belichick has an idiosyncratic fetish for special teams players that no other team has is an almost complete misconception. Go to the Pro Football Reference's snap count for any team and look at who takes the Special Teams snaps. Most every team has 3 or so non-kicker/LS players who take the bulk of special teams snaps and very few offensive/defensive snaps. This Special Teams class of player moves from team to team. Patriots have picked up core Special Teamers from other teams, and vice versa. That's because every team has them, more often than not. It's not Belichick being different.
As one example, I give you old friend Jordan Richards. Remember him? Sorry for the flashbacks. We traded him away in 2017 to Atlanta, where he played his career high in defensive snaps. Atlanta discarded him after that season, Richards played three games back in New England but got released. And then... He got picked up and spent the next few seasons in Baltimore as a pure Special Teamer. In 2020 Richards played in all 16 games taking 79% of Special Teams snaps... and only15 total defensive snaps. Surely no one was thinking of Richards as a contributing safety at that point in his career. For that matter, his fellow 2020 Raven Special teamer Anthony Levine, another supposed safety, who played 30 total defensive snaps at the age of 33 but 70% of ST snaps. The third Special Teams guy on the team was a young UDFA LB, Kristian Welch, who played 173 ST snaps and 8 defensive snaps.
Baltimore, of course, is regularly fellated for it's smart roster construction, and yet three no-hopers took up roster spaces simply so that they could run down and cover kicks. And that's just one randomly chosen team. Most teams, I think you'll find, are constructed this way.