The captain has the prerogative to reject the suggestions of his underlings. The question would then be, what were Picard's motives for rejecting Worf's recommendation? Picard might have had different reasons at different times.It's shown in Star Trek the way Picard consistently denies Worf ...
It should be noted, that as a security officer, Worf's first duty is the protection of the ship and her crew, yet Picard always seems to "know better" than his own security officer.
ETA: I think my problem is the way they made humans the "civilized whites" where the Klingons are "the rest." It makes me, a Hispanic man, very uncomfortable because attitudes like this is very pervasive in society and very hurtful. Culture is important, and TNG had difficulty portraying that in their first seasons.
But in general, did Picard have a low regard for Worf because of Worf being a Klingon? and which then led Picard to deny Worf as often as your video showed? I suppose that's a possibility, if that is what you were suggesting.
I doubt that is what the writers would have intended though, because Picard is suppose to be so enlightened and because in the TNG universe people supposedly don't think that way anymore. But who really knows.
This brings up another question. How did Worf attain his position as weapons officer in the first place? Did Worf get his job because of political correctness of the times? Is it possible that Starfleet wanted to show how progressive they were by having a Klingon in such a high position?
Did Worf attend Starfleet academy? What were his qualifications to earn a position on the Enterprise bridge anyway?
Did stereotyping have anything to do with Worf being assigned to the position of weapons officer? You know, Klingon's have a thing for warfare. So perhaps, stereotyping did exist in the TNG era. But then again, Klingon's did display a fondness for brutishness and combat and crudeness. So was it really stereotyping?
As for Worf, even though he was raised by humans, he still displayed those traits of brutishness and combativeness. Is it possible that Picard had those same thoughts about Worf and therefore had doubts about Worf's opinions? Or maybe we're just reading too much into Picard's rejection of Worf's suggestions? I don't know.