I highly doubt that's true. Email is pretty essential to the functionality of the internet, from signing up accounts to getting notifications, to just plain discussions with professionals. It's pretty much the only thing that does what it does.
To use non-nerd examples people in my life have done recently via email: contacting the school registrar's office, updating insurance information, discussing minor problems with a recent surgery with their doctor. Especially for people with anxiety issues who have problems on the phone, email is a life saver.
I lived off email when buying a house through a builder last year. Everyone went through email and nothing else was even offered in many cases. The builder, bankers, lawyers, electricians, everything was email.