I was recently hired to be a manager at a new company and during my onboarding I was told that there isn't really a promotion process here and it is expected that worthwhile employees will figure it out.
I would question the implicit assumption that the skills required to figure out the workings of an undocumented, informal promotion process are closely correlated with the skills required to be a valuable employee. There might be some workplaces where this is true due to the nature of the work, but there's no obvious reason to believe this as a general principle. To be blunt, it sounds like optimism.
There's also a question about how much time you want employees to spend trying to figure out that process, vs. just being able to point them at the documentation. This one comes down partly to elements of scale - for a small business that only needs to deal with these issues occasionally, an ad-hoc process might be less effort, but for a large one there's more benefit in standardisation.
(There is also an issue of whether a candidate's ability to game the process correlates well with their value as an employee, but that's an issue for both formal and informal processes, albeit in different ways.)
I will note that a formal promotion process doesn't automatically mean depending on KPIs or other such gameable metrics.