Like some others, I have concerns particularly about the elderly and more so in rural areas. America is a lot more spread out than Europe, and our country can be very, very country. Seniors may still be competent to live alone, but may be unable to drive, and while asking me to walk a mile is no problem, it could be a problem even for a physical competent senior, or a moderately disabled person.
I would propose some kind of hybrid. I think that model is probably fine for cities, but until something better is worked out, maybe not for the more rural areas. As TT pointed out, perhaps we could go to tri-weekly deliveries, especially to areas that are too rural for this to be feasible for everyone. But even in cities, we want to make sure drop-off points are pretty abundant, because a lot of smaller-scale America cities don't have very good transit (i.e., using the current postal offices as the drop-off points would be much too spread apart even in most moderate-sized cities).