How can you sincerely suggest remote backups if virtually none of them provide privacy provisions? If anything, people should be discouraged from using remote backups that are not encrypted at source.
Agreed that backing up only in transit can be sketchy. Most online backup services (including ours, www.Backblaze.com) encrypt your data on your client. Also, we provide an option to use a private key in which case not only is it encrypted, but only you have the key. Of course, if you forget it the data is completely unrecoverable.
A remote backup can be very slow to restore, so having both local and remote backups may be worthwhile. It's more expensive, of course, so it's a judgement call, but it's too simplistic to say that everyone only ever needs one of them.
Remote is slow to restore, but it's even slower to back up in the first place. With the current state of not-so-high-speed internet in North America, it could take several weeks to upload 100GB of pictures and videos.
One of the reasons they made March 31st World Backup Day is to prevent data loss in case of a nasty prank on April Fools' Day. Not sure how realistic a threat that is, but it sort of defeats the stated purpose of World Backup Day if your backup won't complete until mid-May.
Also, most remote backup services allow you to restore files and folders selectively, so you just need to download a small amount if you're in a real hurry.
One option that Backblaze (and some others) offer is the ability to order an external hard drive with all your data via FedEx. That way, if you need a terabyte of data back, you get it quickly.
There are only three reasons to backup: Media failure, inadvertent modification or deletion, and loss in the event of theft or fire.
Onsite backup only covers you against the first two.
I have found that people tend to overvalue the value of their data to others and undervalue the value of their data to themselves. Having lost all my data in the third category, I can say I'm never going to bother with an onsite backup again; it's simply a false sense of security.
Remote backups are generally far more expensive – the monthy payment quickly reaches higher than the cost of hard disks. If you only told people of the possibility of remote backups, many would consider it too expensive and give up on backing up, whereas they might be comfortable with local backup.
There are some reasonably priced solutions out there. Backblaze, the company I work for, is $5/month or $50/year for unlimited data backup. Since redundancy is key in backup, both onsite and offsite backups would make up a good backup strategy.