If you're in a remote area, maybe you'd just have to accept mail service that only came by once a week, and maybe only to centralised postal locations.
And maybe you'd also have to accept that anyone who wanted to send you mail might have to pay a bit more for it.
For other areas, why are they proposing dropping Saturday delivery. That means 2 days without mail. Why not drop Wednesday?
Perhaps you could subscribe to a service where a completely automated system could open the original mail, scan it, and allow you to accept an electronic copy instead, for a credit. If you still wanted/needed it delivered, it could reseal it.
That might admittedly be complex to implement in a private fashion, but, I suspect people even in non-rural areas might be excited to have scans instead, so it might pay for itself.
Dunno. Maybe some areas will never be profitable for non-electronic delivery of cheap (say, $1) mail. People living in those areas might just have to accept that paying more for physical delivery of mail is a side effect of living there.
In this case though, the main reason the Postal Service is running out of money is their retirement plan.