Interesting to see a swing in the other direction. About a year ago a mentioned the importance if military presses vs flat benching and received negative responses from multiple individuals.
For athletic improvement in most sports, the standing barbell press is more important than the bench press. It requires your abs and posterior chain to contract in a static fashion while stabilizing your core during the entire movement. This specificity of static strength expression is unique and has a direct carry over to fighting and various other sports.
Dumbells have benefits that barbells don't; as such, do not substitute one for the other given that they each of unique benefits.
Wolverine, do not perform barbell presses behind you neck, regardless of whether you possess the flexibility or not.