Whilst not disagreeing with you, I do question the “bridging” to the car door. I am not sure one sufficient license to make that limud.
I remember hearing a story (R’ Gifter, maybe?, if anyone knows help me out) Where a bochur asked whether he should open the car door for the girl from the outside (and thus let her in 1st) or if he unlock it from inside the car.
The reply was use your head! If it is raining, open from the outside and let her in 1st, if it is hot, open the door from the inside so that some of the hot air had time to escape (and maybe the AC had time to start).
Additionally, IMHO chivalry is dying, and women’s lib has killed it (I’m sure this will open a can of worms). Chivalry was based upon the idea of women being “weaker”, (and thus should be catered to in said fashion) and women’s lib preaches equality. Well, if a man now believe they are equal, why should he buy her dinner, open a door, or kill the mouse in the office, let her do it! She can do anything he can!