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.
Fighting shoulder to shoulder with one of your former enemies shouldn't be anywhere harder than being under the command of another one, right?
Sigh. Shall we squabble over technicalities, now?