This can be a lot harder and more stressful than it seems if the problems in the process are not something the new employee can actually fix and is expected to bug other people to make the necessary adjustments (gaining access to systems and following proper procedures wrt coding style and documentation, in particular). This forces the new employee to immediately become a pain in the ass rather than an actual contributor.

A mentor tasked with onboarding the new employee will be far better equipped to be responsible for tweaking the process. (Whoever actually pushes the buttons matters less than who owns the job in this case). Too often a new employee facing an onboarding problem will be stumped not even knowing the right question to ask. Leaving them to figure it out on their own is horribly inefficient.

I have seen this nearly every place I've worked and inevitably, it's months before the new employee actually acquires the mundane institutional knowledge, relationships, and perspective required to effect the necessary changes, meanwhile there were plenty of other options for worthwhile contribution that don't involve fixing an onboarding process that should have been someone else's repsonsibility.