I wouldn't call it nuts but one must choose to draw the line somewhere.
Each of us has our own comfort zone with a car care. Typically it's roughly in between a windowless climate controlled cleanroom, only touching it with microfiber gloves while wearing a Tyvek suit and reenacting every other driving scene from the Dukes of Hazzard.
As beautiful and finely crafted as Aston Martins, Ferraris, etc are they are built to be driven and enjoyed. I insist on taking off my shoes every time I enter my house because I feel there's a distinct delineation between being inside a home and being out in the world. I would not want to do it to go out for a drive (if it were my car that is, as a passenger I would certainly respect the wishes of a car's owner).
I would much rather buy a new set of floor mats every year (and a shop vac and carpet extractor to keep them looking good in between). Maybe having a separate set for those muddy times of year would be a good idea.
The paint protection film can be similar. It isn't attractive. It never looks good or "right". In some applications it can look like the cheesy plastic covers Aunt Edna put on the furniture in her unused living room. At best it's not too noticeable.
I did put it on our MINI because I wanted to drive it across the desert and alternatives like massive pitting or new paint every year were less desirable. A door handle is small enough that it might well go unnoticed. Or, it might stick out like a sore thumb since you walk straight up to it every time to approach the car. It's certainly worth a try. It's cheap to try and easily removed if it doesn't work out.
PC.