Like most areas of fitness, it's pretty easy to find conflicting advice. That said, I think most would agree that keeping the bar as close as possible to the legs on the way up allows you to lift more weight, but that actually hitting your shins or knees can hurt, and may also be suboptimal due to introducing friction between the bar and your legs. Keeping the bar close to the legs is optimal, because it maximises the proportion of the load that can be shifted from the hips and lower back to the legs. Whereas lifting with the bar away from the legs very quickly puts the entire load only the hips and back.
In powerlifting, the standard practice (generally required in competition) is to wear long socks in order to avoid drawing blood (and creating a disease transmission risk) during the deadlift. Those who really tend to pull hard into their shins will also often wear strips of athletic tape up the shins, underneath their socks.
Practically, I'd usually advise that people deadlift in tights, pants, or long socks, or if they find that they get too hot with their legs covered, try to start the lift with their shins in contact with the bar, but then aim to maintain only slight contact on the way up. Maintaining light contact with the bar should be achieved by straightening your legs only just fast enough to keep them out of the way of the bar, not by allowing the bar to swing forwards.
As for the individual sources you reference:
- Everything in the Brentwood Barbell video seems like good advice.
- The second video you mentioned is missing its link.
- Pheasyque makes the assumption that when the spine flexes, the hips and knees remain in the same position but the shoulders (and hence the bar) move backwards. This is extremely unlikely. It's not hard to find videos of people letting their spine flex as they begin the deadlift, and pretty much whenever this happens, it's a matter of the knees straightening and hips rising, while the shoulders stay in the same position. So in that case the shins are actually getting further away from the bar.
- The Women Who Lift Weights video just seems wrong from start to end. Long-legged people don't deadlift with vertical shins and short-legged people don't have a tendency to start with their knees further in front of the bar. When he says this, you can actually see that he pushes the bar forward in order to get his knees forward, which reveals the real cause of having the knees too far forward in the deadlift - starting with the bar too far forward. Then we he demonstrates "getting a little bit back from the bar", he actually pulls the bar back over the mid-foot, closer to his standing shin position.
- The Athlean-X video actually says that the bar should contact the shins the whole way up. From 12:08: "We want to make sure that it's dragging up those shins every inch of the way. Alright? Staying in contact."
