It can be quite high, but it doesn't have to be. For instance, I have a 7TB storage server from Hosthatch that's $190 for 2 years. That's $7.92 per month, or £5.88 at today's exchange rates. That's under 20p per day.

Just on electricity costs alone, this is good value. My electricity costs are 22.86p/kWh which is pretty cheap for the UK. That means that if having that drive plugged in and available 24/7 uses more than 37W, it's more expensive to self host at home than rent the space via a server. Also, I've not needed to buy the drive or a NAS, nor do I have to worry about replacing hardware if it fails.

For very large amounts of data, the cloud provider can hit economies of scale using tape drives ($$$$ to buy a tape drive yourself) or enterprise-class hard drives (very loud + high price of entry if you want redundancy + higher failure rate than other storage). That's why storing data in the slower storage classes in S3 and other object stores is so cheap compared to buying and replacing drives.