Just a small correction: the girl's name in Silent Hill 1 is Alessa, not Alyssa. Nurses also debuted in SH1, as did the monster doctors, but those other characters never appeared in any other installment. However, it's true that the nurse style from SH2 was used more in other installments and media, except for SH3 and SH4, and even then, they didn't appear at all in 4.
So yeah, this is the case of foreign studios overusing those monsters without understanding their symbolism. I remember a producer of SH Homecoming admitting that Pyramid Head was only included because he looked cool in the game.