It’s not black/white as having backups solves ransomware attacks. All that the ransomware must do is lay low long enough that the oldest backup is likely to have occurred after the infection, hence containing it.
For a ransomware to propagate that way it would have to employ multiple exploits against unknown operating systems, and against computers managed by people who should have some idea about security rather than just the desktop of a random employee. In many cases you'll be backing up to storage provided by a 3rd party who simply don't even offer the capability to run code, or permanently delete data programatically.
I'm waiting until ransomware starts leveraging the encryption functionality in common backup systems. Not many sysadmins would notice if their backup encryption keys were changed-out for 6 months and deleted at the same time that the "encrypt all the data" event happened. (The only Customers I've ever worked with who were already doing air-gapped backup verification were regulated businesses in the financial sector.)
It would be pretty hard to get your ransomware to encrypt all those offsite backups sitting in a vault somewhere.
If you use thin clients or at least require all files to be stored on a centralized server, then no matter how many hundreds of PCs were affected, you'd only have to go through on set of images.