I have to agree with the previous message, that banning mail from the building will immediately cut off access by the general public (not just the elderly or the poor) that newspapers allege to serve. But it is not so much elitist as it is thoughtless and panicky (much like a lot of news coverage these days). Hey, maybe papers should allow the public to dictate their Letters to the Editor! "Got something to say? Leave it on voice-mail!!"
Seriously, it would be far better for papers to figure out a practical/safe system to screen and handle mail that does come in (and help publishers avoid workman's comp or wrongful death suits from poisoned staffers, which may be their bigger fear). I imagine the Post Office has some thoughts on the matter.
Meanwhile, there's nothing wrong with reducing the volume of mail by requiring press releases and other forms of business correspondence to be delivered electronically. Most businesses today have the means to handle electronic communication. But papers will have to prepare for a short-term bottleneck of information and long-term extra expenses. Papers will have to set up systems for electronic payment of advertisers' accounts and home delivery bills. They will have to hire additional personnel to screen the sudden flood of new e-mail (or they'll have to upgrade computer systems to allow this to take place). Editors will have to prepare for an an onslaught of new "did you get my..." phone calls. And papers will have to shell out much more for fax paper as they absorb the cost of mailings from PR firms. And on and on.
Like anything else, the first, quick solution is rarely the wisest. Watch for back-pedalling inside, say, three months.