Petri nets are a BPM notation. Unlike many other BPM notations, Petri nets have an exact mathematical definition of their execution semantics, with a well-developed mathematical theory for process analysis. For this reason, they are popular in academia. Probably for the same reason, they are rarely used in practical BPM modeling, apart from very specific and complex analytical tasks.
Notations as such do not represent laws or metadata but just serve as a form of expression. Similarly, one physical law can be written in several complimentary formulations like in quantum mechanics. It is only essential that each BPM formalization correctly represent the reality of organizational structure and business operations. If this rule is observed, models drawn in various notations will ultimately converge to singular representation of a business, which they represent.
Simplicity is mandatory, especially in context of end user interactions. However, it is important to distinguish a simplicity arising from deep understanding of the subject and ability to formalize it in simple terms from a simplicity, which emerges from poor awareness on relevant business domain. Needless to say, real organizations can be very very complex. It is then an art and professionalism of consultant to formalize and represent them in a simple and logical manner.
Surely, Petri nets for end user modeling can be an overkill. However, same Petri nets and much more complex structures might be entirely relevant as a hidden technical implementation. Again, the task is always to represent the real business structure and processes of organization in most compact and efficient form, whatever notation and methodology will be most relevant for this goal.
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