At this time, no public API truly allows for the retrieval of every activity and update that appears on an object's timeline (contact, company, deal, or ticket). The team is considering this kind of feature in the future, however.
In its current state, the Tickets API assumes integrators are storing historical values in their systems. In these circumstances, the Get a log of changes for tickets endpoint is polled periodically and the integration takes the
changedProperties and queries this or this endpoint to retrieve the new values for those properties (as opposed to a single endpoint returning all historical values for a property every time).
Apologies for the inconvenience; I realize this isn't the exact solution you're looking for. I've made a note of your feedback as the team continues to iterate on the Tickets API.