Couldn’t the batteries be used as backup power?
Moot point if the DVR system is operating on backup power and also powering the cameras.
Battery powered cameras were marketed to DIYers and renters to simplify installation (cabling can be complicated, and expensive if done by professional low voltage technicians...at least that’s what they want you to think). I never considered them viable; proof is in the OP, insofar as serious security is concerned.
There are many options for installing cables without major modifications to structures, but the larger questions of security go much deeper than wired/wireless...
Bottom line: Wireless is still viable for renters and residents, but clearly it is advisable to have at least one wired camera.