Also, there's a saying.
"The enemy of my enemy is my friend."
I'm prety sure that regardless if their affiliation is Allied or Axis, none of the ships want to be sunk by Abyssals.
I wouldn't want my girls feeling uncomfortable. There's a chance that if, say, Kaga and Enterprise would sortie together, Kaga would want to trounce Enterprise in terms of kills, causing her to be more reckless. There are a lot of scenarios which could go wrong. Heck, put me in a team with a person who I've had a history of bad blood with, I'd be uncomfortable. Even if we were fighting against a common enemy, I still wouldn't like the said person, and I'm sure some of the Japanese kanmusu would feel that as well.
A lot of warships sunk during WWII were actually victims of aerial attacks from the carriers, or they were so damaged that their allies had to sink them later. Well, granted, if USS Portland was added, I'm pretty sure that there will be way more than bad blood between them...
Competition could be. But knowing Kaga's pride, I'm not surprised if she wants to win in that regard, even if they aren't enemies anymore.
And frankly, I'm sure they have some vague recollections of their past lives. Vague, sure. But some of them may remember the ones who defeated them. As the saying goes "Keep your friends close, and your enemies closer."
I may be judging too early, and I hope it doesn't cause offense, but it seems to me that you're one of those persons who think of persons/things as a "means to and end" sort. And that's where we differ. And it's pretty much why I dislike the idea. If they help, sure. But, I can't say I'd welcome them with open arms into my fleet.