It would make sense for Pike to decide to give Kirk authority if he thought Kirk's approach to the current crisis was decidedly better than that of any of his other officers or officer-replacements. But the way he did it is a bit odd.
He doesn't tell his officers "Kirk here knows what to do, he's in charge now". He tells them "I like this Kirk guy here, so I'm sending him to this suicide mission while you continue to be in charge, Mr. Spock". That's the exact opposite message to the one Pike would give if he told Kirk "You have the conn now, Cadet/Lieutenant; Mr. Spock, make sure our ship does her very best to accommodate Cadet/Lieutenant Kirk's needs, whims and cunning plans".
I can sort of understand that Pike would get, if not cold then at least lukewarm feet, and leave things halfway: not giving Kirk the conn outright but subjecting him to moderation by Spock would be a reasonable compromise. But making Kirk the 1st Officer is an odd way of making him Spock's trusted advisor and second-guesser, because it places him in the line of succession when there's no real need to do so. Kirk gets both too little and too much at the same time...
Timo Saloniemi