As far as after landing runway incursions up until a few years ago, it was our company’s policy to not allow the FO to perform any after landing duties until inside the perimeter of all runways. This forced the FO to “stay with the Captain” as he or she crossed all intervening runways.
We have since relaxed that to, “when situational awareness and time permit, normally when clear of all active runways.” Sometimes with senior FO’s I have found they are so skilled and intent on doing their after landing flows, they forget what is most important in the moment - cleaning up the aircraft or making sure I don’t screw up and inadvertently cross a runway. As part of an approach briefing, threats such as after landing potential runway incursions should be acknowledged and briefed and the FO reminded to “stay with the Captain” until an appropriate time to do after landing duties.
As for taxi out, a pre brief of potential taxi routes again can address potential threats as long as one doesn’t become fixated on the brief versus actual clearance. (Been flying (and flailing) out of KORD for nearly 30 years - as Check Airman stated there is always a potential for a surprise 😄
Captain’s need to practice good cockpit management (for example don’t call for a checklist when you need your FO looking out the window, refrain from taxiing single engine in low visibility, etc) and appropriately brief runway incursion threats unique to each individual flight.