^^ I don't think it's quite that extreme, but she does feel rather shoehorned in. They would do better to go back to her Episode 1 hairstyle and replace the spike heeled boots. As is she's straying into Troi territory.
It could be worth seeing some scenes where she does overstep boundaries. The "real" McCoy would have no problem reigning her in particularly since as a psychologist she falls under his authority. Neither would the "real" Spock.
Another factor could be not quite having a handle on how to write Spock and McCoy, the dynamic between the two of them and their relationship to Kirk. Also fan fiction has long been known to focus on one or two favoured characters sometimes at the expense of the others---and fan productions are essential fanfic fully realized.
It remains to be seen what they'll do with McKennah. If the STC folks are indeed aware of this discussion as well as others in other forums as well as their Facebook page and feedback through their own website then they should see the general reaction to the McKennah character. Then it's a matter of whether they adjust or temper how they utilize her character.
Small note: in TOS the Enterprise
was not a flagship. That notion started with TNG.