Benefit of Petri Net Transition as Separate Object
The state transition graph underlying a Petri Net model is called the Reachability Graph. Yes, it exists, and it is the foundation of Petri Net semantics. However, it is possible to define simple, easily understandable Petri Net models that have reachability graphs of a size and structure that no human could make sense of. They might also be graphs with an infinite number of states.

It's similar to programming languages: every conceivable algorithm or program could be written in assembly language. But there are dozens, if not hundreds, of higher level programming languages that make it easier, simpler, and faster for humans to write and understand programs, to express the algorithms and the processing they need to implement. And then a compiler or interpreter turns the high-level program into a stream of processor instructions.

Petri Nets are meant as a way for humans to create meaningful, understandable models, without drilling down to individual states and transitions. Then Petri Net tools handle the simulation and/or analysis of the models.