Most consumer doorbell cameras send recordings to a server rather than keeping them on the device. The choice is driven by power, hardware cost and the business model built on both.
Local storage requires the device to stay awake
A camera holding its own recordings must also serve them, which means keeping a network service running and responding whenever a phone asks for footage.
Battery-powered devices instead sleep almost continuously, waking on motion, transmitting a clip and returning to sleep within seconds.
That duty cycle is what allows months of runtime, and it is incompatible with acting as an always-available file server on the home network.
Processing moved off the device for the same reason
Distinguishing a person from a passing car requires computation, and running that continuously on a battery device would shorten runtime dramatically.
Sending the clip to a server allows heavier analysis without any local energy cost, and lets detection improve without replacing the hardware.
Newer devices increasingly do simple detection locally to avoid uploading uninteresting clips, which saves bandwidth and battery simultaneously.
Remote access is the feature users actually want
Viewing a doorbell from elsewhere requires reaching into the home network, which is awkward and insecure to arrange directly.
A server in the middle solves it cleanly: the camera connects outward, the phone connects outward, and the service joins them without opening anything.
Local-only devices have to solve this with a hub, a dedicated app, or user-managed network configuration, which most buyers will not do.
The subscription funds the hardware price
Storing and serving video is an ongoing expense, so devices sold cheaply are generally sold with the expectation of recurring revenue.
Without a subscription, many cameras retain only brief recent clips or live view, which is enough to be useful but not enough to serve as a record.
Cameras with local recording cost more upfront because the storage, processing and continuous power are being paid for once rather than monthly.
Retention policy is where the real difference lies
Cloud storage keeps footage for a set number of days, after which it is deleted automatically regardless of whether anything of interest was recorded.
Local storage keeps footage until the card fills and then overwrites, which places retention under the owner's control and away from the provider's.
Access requests and law enforcement procedures differ accordingly, since a provider holding footage can be asked for it while a card in a home cannot be queried remotely.