This is what I'm thinking -- that it's more important as a way of connecting with the world as kids get older. People certainly managed just fine without it up until recently. I didn't even learn to browse the Web or send emails until I was in my late 30's.
That said, whether homeschooling or public schooling (our 8 year old dd is still unschooling but our 13 year old dd wanted to start public school so she did so this year), I feel like it could be kind of a handicap for a teenager today not to have any Internet access. I'm sure it could be worked around by frequent visits to the library -- and for a child who loves country living, the joys of living in a remote rural area with no Internet access could easily compensate for the loss of that connection. And I do realize that spending too much time connected to the Internet can take away from the time we spend enjoying face-to-face contact with family, friends, animals, and the great outdoors.
So maybe not having Internet can even be a good thing for some families. It's something each family has to weigh out for themselves. For us, being very low income and not having money to buy a lot of resources, including entertainment resources, the Internet has been priceless as a way of paying just one fee and getting to enjoy things like music and Vlogs on YouTube and also movies that are public domain now, and can be viewed for free. And finding out about giveaways on Craig's list, and so on.