I don't necessarily love it as a characterization because Americans also have a love of huge refrigerators and couches and washing machines but no one says we have a refrigerator culture (even though it may be true). When you think about the number of boring base-level Corollas that get sold, it's hard to think of it as an identity thing.
I think a fairer description would be that American culture values space, personal property ownership, and independence. Car ownership is a means to an end.
I think the larger size of appliances and furniture in the US isn't because of any particular love of larger sizes for those things, just that suburbia tends to give people more room. I'm not sure of the direction of causation: do Americans value space and personal property ownership and independence on first principles, and then spread out in large house on large plots of land because of that? Or did those values grow out of the incidental ability to have lots of house space?
Our fridge/freezer is on the larger size, but is also usually pretty full, so we definitely get good use out of it. Our washing machine is reasonably large, but, frankly, not large enough, as I can't fit our king-size bed's comforter in it, and have to use a laundry service to get it washed. Our couch is a pretty good size, but my partner and I want to be able to stretch out on it (at opposite ends) simultaneously, which doesn't seem like a wild or unreasonable thing to want to do.
And I prefer a smaller car! I refuse to purchase an SUV, despite my need to drive in snowy mountains several months out of the year (I of course found a sedan with a 4WD option). I hate driving SUVs; they feel bulky, unwieldy, and unstable to me. Before I bought my current car, I would rent a 4WD SUV when I needed to drive in the snow, and I hated the experience every time.
Car ownership is not really independence. Eg. It isn't very independent to sit in traffic with a crowd of other car owners, waiting for them to move so you can also move. Then you are also dependent on fueling stations and other infrastructure.
I think a fairer description would be that American culture values space, personal property ownership, and independence. Car ownership is a means to an end.