I don't think there's a law mandating it, but CRM (https://en.wikipedia.org/wiki/Crew_resource_management) has been used and trained by all major airlines since the 1980s. The reason is simple: it doesn't really help to have two people in the cockpit if only one of them is making all the decisions.
And all Military air forces AFAIK. The military of course also takes rank very seriously, but there was existing understanding that Mother Nature doesn't give a shit about rank and so CRM makes sense in that same practical vein.
Also, you'll see that says "Crew" not just "Cockpit". Turns out that from the cockpit of an airliner you've not always got the best possible view of the problem. If the steward who has no idea how to fly a plane insists it's the right engine that is on fire, her input is valuable, from back where she's serving customers with coffee she can see the engines, the fire is on the right, whereas you're just looking at sensor outputs and you were maybe about to turn off the left engine.
I don’t think it’s required, but my friends who do flights for remote mining operations in SE Asia use the same concepts — so it really is pretty standard for commercial flying, even down to remote private operations.
A bad bump on a commercial plane can be hundreds of thousands to millions in damage + downtime + inspection/repairs. And tens or hundreds of millions if you wreck a big plane. Companies may be evil, but most would still prefer you waste $2k in go around fuel than $200k because you decided to set it down badly or $20M+ because you drove their plane off the runway.
The reason I ask is, case in point, do you think the PM is going to be penalized in some way?