"This is your bank/IRS. There's a problem with you account/taxes. If you don't respond by date X we'll close/fine your account/you. This is the only notice you will get."
Neither banks nor the IRS use email for that. You know who does? Rackspace, which sent me a pair of emails recently informing me of tickets they had opened which I should probably look at. It turns out if you don't respond to an Acceptable Use Policy violation they'll turn off your servers and close your account.
They sent one reminder, which I also missed. By happiest of coincidences, I logged into their ticketing system to look up a Linux command a support rep had taught me once, and saw the tickets.
(The AUP violation was a server getting hacked, probably via a WordPress blog, and being used to attack SSH on other servers. I nearly had a heart attack, until I realized "Hey wait, that is not actually an IP I own." Turns out they had the wrong account. "Sorry about the mistake!" I don't think that would have cut it, honestly, if they had actually gone through on the deactivation threat.)
You will find that that is not actually true. You cannot opt to get certain communications via email, partly due to regulations and partly due to banks actually wanting people to read certain high-value communications. One type of many is the FCRA notification of adverse action taken in response to pulling a credit report.
Not legal in sane jurisdictions. There is no guaranteed delivery of email. Important stuff still needs to be sent by confirmed fax, or snail mail with various options to confirm delivery to the recipient.
Where do you draw the "important"-line? Most my (important) bills come in my snail mail mailbox without any confirmation to the sender. If i don't pay them on time i get a delay fine. What's easier, pay the fine or try to prove in court that you never received the invoice? Or worse, explaining that you threw out all the mail you received during holidays?
Still, I agree, important messages through email should always be replied to to confirm that you've got them.
