The biggest limitation is quite simply bandwidth.
For a majority of connections, the initial upload (possible hundreds of gigabytes) is infeasible. Even the "unlimited" connections are most certainly not, and almost all have fair-usage policies which would hinder such transfers.
Also a service receiving hundreds of gigabytes of data from hundreds/thousands of customers seems like a fairly crappy business..
There are such online backup companies (there's loads, like Mozy and Backblaze), but I can't work out how they make enough money to pay for the storage/bandwidth/staff - offering "unlimited storage for just $5" does sound too good to be true, and seems like it is..
Backing up to something like Amazon S3 (or rsync.net), which charges based on the amount of data you store, seem more sane - but Mozy has been around for a while and does seem to be doing quite well