This is basically the Event Sourcing pattern. You start with an initial state, keep the events relating to it that might change it, and thus the current state can always be found by replaying those events. In the example above you don't even need to replay them in order, although maintaining order is definitely useful in more sophisticated uses of this pattern.

Double-entry book-keeping is done this way. The data certainly grows over time, but generally at a predictable and manageable rate.

Most people using long-lived event-sourced data structures have some kind of snapshot/checkpoint/archive mechanism, which going back to the accounting example might simply be an opening balance.