The real answer to the question whether the Postal Service is worth what it is costing can be found only when various indirect government subsidies stop and when the government stops forbidding others from carrying the mail -- if that ever happens.
If FedEx, UPS or someone else can carry the mail cheaper or better than the Postal Service, there is no reason why the public should not get the benefit of having their mail delivered cheaper or better.
Politics is the reason why no such test is likely any time soon. Various special interests currently benefit from the way the post office is run -- and especially by the way government backing keeps it afloat.
Junk mail, for example, does not have to cover all its costs. You might be happy to get less junk mail if it had to pay a postage rate that covered the full cost of delivering it. But people who send junk mail would lobby Congress to stay on the gravy train.
So would people who live in remote areas, where the cost of delivering all mail is higher. But if people who decide to live in remote areas don't pay the costs that their decision imposes on the Postal Service, electric utilities and others, why should other people be forced to pay those costs?
A society in which some people make decisions, and other people are forced to pay the costs created by those decisions, is a society where a lot of decisions can be made despite their costs being greater than their benefits.
That is why the post office should have to face competition in the market, instead of lobbying politicians for government help. We cannot preserve everything that was once useful.