One Drive is working for me just fine on my iPhone, and there are other options available like DropBox and Google Drive as well.

iPhone doesn't not allow phone backups using another cloud provider? Are you talking about backing up images?

Yeah sorry, thought that’s what you meant.

For whole phone backup it’s either iCloud or hook it up to a computer.

Does Android allow whole phone backups to third parties without rooting?

Using Itunes........with android you can literally select another CLOUD provider.

Yes because with iOS you can also RESTORE your entire operating system from that same backup. And if you really want to, you can change the file location so that iTunes backup file sits in a cloud folder.

I back up data on my iPhone to my NAS using a third-party app.