Verlet integration became the go-to method for particle effects and soft surfaces back when people wrote their own game engines, mostly thanks to the paper documenting its implementation for the first Hitman game [1]. In fact, I'd say it got cargo-culted by game devs for that purpose and that purpose only, despite it being a general method and competing with others.

[1]: https://www.cs.cmu.edu/afs/cs/academic/class/15462-s13/www/l...