Right; project management is really more about facilitating communication than anything else. Most projects have lots of domain experts who each have an idea of how things should be done. A good PM's job is to facilitate the conversations that need to happen to get everyone to agree on a plan, then communicate out the plan of record to everyone. This has the bonus factor of being able to peer-shame anyone who decides to deviate from the agreed-upon plan; which is helpful because in most organizations PMs have no real power to do anything.

And a management tool won't make a bad manager better, they'll manage just as badly through the tool. It can actually make things worse if you're the manager of a bunch of managers who all use the tool differently: your reports from the tool will be meaningless at best. That's why my preferred approach is to add project management to a workflow tool; not the other way around (e.g. we don't make development leads enter their tasks into MS Project, we put the project tracking info in Jira and manage it through there.) That way you can drive data consistency through process consistency and not piss off your developers by wasting time with multiple systems.