At the place I fly I'd estimate about 10% of the captains have the really old school captain mentality that is still prevalent in some Asian carriers. "You are the FO, I'll do as much as I can as captain but if I need you to do something then I'll ask you."
Sometimes it is the little things and sometimes it's not. Taxiing in I'm looking out the window as the captain taxies through the ramp and as I'm looking out the right window at some ground vehicles, the plane jerks around a little bit so I turn around and see that, while steering the plane with his left hand, the captain is reconfiguring the bleeds and packs and shutting down one engine with the right hand stretched up and across the cockpit. I'm sitting in the right seat, directly beneath the switches for that stuff with both hands free...why not ask the FO to shut down the engine? Not once in 100+ jumpseat rides on a legacy carrier did I see a captain reaching across and shutting down an engine while taxiing and not telling the FO about it. It's a two-pilot airplane and the captain has no need to be taxiing and doing much else at the same time through a busy ramp.
Here's another one -- holding patterns. We're holding to get into a hub and the weather is good but the volume of traffic has caused some delays. Our EFC time is a bit lengthy but it seems like it won't hold up. Because the weather is good, however, we don't have much extra fuel at all. The captain, while flying the plane on autopilot in the hold, pulls out the release and starts running the numbers to see when we've got to leave the hold. Meanwhile the airspeed has decayed to less than it ought to be in the turn heading outbound in the hold so I ask, "I can fly it around the hold here until you're done with that." I get a look back like, wow that is the best idea I have ever heard. Well hello, I'm sitting here doing nothing! Then when done with the number crunching he shoves the release back into where it was and informs me of the amount of gas we'll leave with. I give him the plane back and reach for the release and get questioned about what I am doing with it. Well, I'm going to do the numbers too, and see what I get! How am I ever to know how to do that if I never look at the numbers during a hold. But from this I assume that there is a sizeable chunk of first officers here that don't get involved enough in decisions such as this example.
I thought of those two examples after reading the stuff above about some regional airline captains being the way they are as far as willingness to educate their FOs. I truly believe some of them started out as captain willing to teach and willing to use the first officer more as a resource than they currently do because they are simply tired of being the captain instructor.
I can just imagine the thought in the one's head about shutting the engine down. He probably had a few first officers in a row that he asked to shut down #1, and they did something wrong with the bleed or pack configuration, and he had to adjust it afterwards while taxiing, and after a couple times of that he just figured, "screw it I'll just reach over and do it myself and they'll see that the engine has been shut down."
I suppose this comes with having low-time FOs in the right seat who are new to jet aircraft and any captain who is the least bit impatient at educating them is just going to get lazy and give up after a while. Eventually they become the 10% that I think run the cockpit with a much more single-pilot attitude than they should.