iCloud backups are not necessarily a paid service. I'll grant you that 5GB is not nearly enough for today's world, but you can back up the core data on our phone in that space for free. 200GB of iCloud storage is $2.99 / month. That really should be the new free tier.
There are also several third-party cloud backup options for iOS. iDrive, Backblaze, Acronis to name a few. There is no reason for Apple to embed a third-party into the core backup. Perhaps they might stand up a new API to more tightly couple, but still, not required by any competitive landscape.
Also, Cloud backup is not the only option. Apple could just take away iCloud backup altogether and have no need to add Dropbox. All backups are local like in the old days. Still not anticompetitive. Stupid and a bit user-hostile, but not anticompetetive.