How does that model fit with the conflicting goal of trying to limit one's carbon footprint?
Current system: a limited fleet of vehicles traverses a prescribed route to distribute to hundreds/thousands of locations.
Your system: someone from every household drives to their postal center.
Plus, what about people who are mobility impaired, who don't drive, who don't have bus service which would get them there?
That model falls apart rather quickly.

I will agree there is obviously less and less need for daily delivery to all residential customers. The vast majority of what I get in snail mail is junk mail and bills, both of which are hardly so time critical as to need daily distribution -- thrice, twice, or even just once a week would be nearly enough for me. Even for business mail, I'm doubtful how much snail mail is still that relevant. Anything information is primarily handled online (email, attachments, web-based dedicated transaction screens, etc). Physical goods (and other stuff not transmittable or for whatever reason not chosen to be handled via electronic media) are more an more likely handled by 'on demand' or other scheduled services from UPS, FedEx, or good old USPS. Thus, I have little doubt in the very near future we will see USPS cutting services (especially residential delivery) way back. Unfortunately, in itself, cutting services is a terrible business model, as it represents a downward spiral -- less customer service >> fewer people will continue to use service >> further cuts in service >> fewer yet will use >> ... .

So . . . super simple to suggest 'just privatize it' -- dump USPS altogether and let private enterprise handle it. Problem is, that works fine in high-population-density (cities), but no private enterprise is going to serve lower density (rural) areas unless mandated (regulated) to do so.