I spent my last 30 years working for a company that is very close to the USPS. Most of you see evidence on my company or possibly a competitor 6 days a week. I have seen major changes in the USPS over the years.
When it comes to letters addressed to a local resident being routed via some central sorting center? That is easy. Some years back equipment was designed to read both hand written and typed or computer based printed addresses. It is call OCR, (optical character reader ) This new technology basically eliminated the sorting of mail at a local level as these machines can read and route letters at a rate of 10K to 20K an hour. It was economically not feasible to employ mail sorters at the local Post Offices. Thus even though it would seem odd that a letter that is local gets routed sometime hundreds of miles away, it is logical when one considers the overall mix of mail processed today. Letter mail is decreasing. Flat and package mail is increasing. So when you hand address a letter to Aunt Sue that lives three blocks over, unless your writing is absolutely atrocious, it is likely that once it is in the system no human hands touch it until it gets delivered.
The other big concern is cost. Some ask why not let the USPS become private like other carriers UPS / FEDEX / Etc. But these other carries do not have low cost letter solutions and therein lies the problem Letter mail is decreasing as more and more of us use email to communicate with family and electronically pay our bills. So the volume of letter mail is increasingly being made up by advertisement mail. Mail that is provided at a discounted rate. In general letter mail is not profitable. Especially when one considers rural delivery. Even the package carriers charge a premium for some areas of the country and in some cases they may not even deliver to them. There are even some programs like FEDEX post to deal with some of these issues. FedEx Post is a service where FedEx gets the package, but the USPS delivers it. There is a UPS program like this as well.
Bottom line. Letter mail is not profitable and that remains the stumbling block for the USPS becoming a private for profit corporation. Now if letter mail could be rated based on zipcode and rural factors, like flat and package services, then the game changes.
The USPS is messed up no doubt. But what if there was no USPS? Who is going to take up the letter based mail? Who would be willing to pay what FedEx or UPS charge for an overnight or even a 2nd day letter to send a thank you card to Aunt Sue?