Starting out that this is still a new Trek, I think it'll take just a little more time for the new Big E to become "characterized", so to speak. Right now, she's just a vehicle for the actual "characters" (Kirk, Spock, McCoy, and all). But, as we come to know her quirks and functions through the sequels, she'll start shaping up into a "character" of her own.
I mean, we don't really view ships or other objects (be they titular or not) as characters until we've seen a few episodes or a couple of movies.
By the time of "The Empire Strikes Back", the Millennium Falcon became more of a character. She was a bit cranky sometimes, and Han kinda paid for it...but she more than made up for it at the Battle of Endor.
Hell, in the tv series "24", after a short while, I kinda looked at CTU (the base of operations for the Counter Terrorism Unit) as a character. She was the shelter of our heroes, and provider of information to help them fight terrorist scum that threatened our country.
And of course, it's up to the individual as to whether or not a ship or object shapes up into a character for them. Some will of course see the new Enterprise as evil, and as simply part of a larger machination that somehow raped their childhood, or ran over an old friend.
That's why I don't allow myself such devotion to shows and movies. I love the shows and movies dearly, but I don't let myself get devoted to them. Things change over time, so there's no point in hanging onto a past that doesn't matter. There are far bigger things in the world to get worried about. (But all that in this last paragraph is another discussion).
Make sense? Sorta?