Ironically, I think the junk mail is going to be more important/valuable to businesses in the coming years and the USPS can make money from it if they price the product right. Advertisers still need to reach customers, and with the rapid "self-customization" of most media streams, it's hard to reach a broad local audience anymore. Newspapers are on the decline, TV is too fragmented and expensive, online ads are similarly channelized and ineffective for local businesses. Direct mail (and radio) are among the only remaining means for local businesses to "broadcast" a message among a local audience. We all still go to our mailboxes.
Advertisers will find ways to reach us. If you increase junk mail postage costs, advertisers will reconsider other channels for their "product." Will probably more online if they increase postage too much. You have noticed that you get ads inserted in other mail, like monthly bills, and even ads from your credit card company in separate envelopes.
And you mention TV is "too fragmented and expensive" - have you noticed there are more and more embedded ads in TV shows (and movies)? You see actors drinking Pepsi, Coke or whatever where it would have been a generic soft drink before - that's advertising. You even see actors mentioning products by name now 'would you like a Coke?' It's so subtle that many people don't notice it.
You also notice that most shows use one make of car exclusively for all characters, Bones for example is all Toyotas. I even remember an episode where two characters were driving a Prius, and they spent about 10 seconds talking about the Lane Keep Assist option. They explained what it did and showed the dash display, all carefully scripted of course. I don't think they've given up on TV or movies, more embedded stuff there too.
I agree with you that newspaper are a lost cause.
Not sure I agree on online ads. I know online ad revenues overall are up. And I think sites like Facebook, Twitter, Google, Huff Post and many others make tons on ad revenues. As for local, the same thing will happen (is happening?). The little population 29,000 town I live in has a website, let's call it Anytownlife.com, that started a few years ago. The site isn't anything special, it list comprehensive events and local interest stories. There are local ads on it too. The guy has a handful of employees, his personal vehicle is covered with ads with Anytownlife.com on it to get the word out - and that's really worked to get everyone to look initially. And he's making a very good living at it judging by his house. I ate dinner with him at a wedding reception about a year ago, and I know it's his only source of income.