Why map at all
Two reasons, and only two. First, so the pipeline data means something, which requires everyone to agree what each stage represents and what evidence is needed to enter it. Second, so improvement has a target: you cannot fix a leak in a process you have not described. Everything else that gets attached to these exercises, alignment, visibility, standardisation, follows from those two.
The failure mode is a session that produces the process management already believed in, drawn neatly. That document has no relationship to what happens on Tuesday afternoon, and within a month everyone is back to the real process, which remains undocumented.