There are no story reasons for Type IIs to need to exist. To be frank, Yorktown could have received a retrofit to signify her return to health or could have returned as is. Same as Hammann, her Retrofit could be retconned to be her healed form. Or they, like Hiryuu, Souryuu, and Shouhou, could have been left as dead and sunk. While Hornet, given her presence in Operation Siren wasn't critically injured. And none of this addresses why they choose to introduce Type IIs, the USN has plenty of ships without them. And no, I have no hard evidence besides having seen how they treat the Starters for 4 and a half years to say they'll be given Type-II Forms.
However, look at Prinz Adalbert. A ship that might as well not exist given her presence. I think they realized that Yard Numbers and Paper w/o Names are very hard sells. Or look at Suruga...who had a Game and a Raid Event behind her, headlined an Event, and was Manjuu's first Paper ship in-game, and was highly anticipated....and almost disappeared after her event with the only exception being one very dedicated fan. Suruga was lucky, she got Kii and Shimakaze to play off of. But Nameless Yard Numbers like Suruga and Adalbert are hard to keep in the public eye, thus hard to sell skins for.
Real Ships with Real Histories have enough trouble. If Hornet II was any other Essex, she wouldn't be half as popular, as to most players, she'd be just another Essex for the pile. No one would probably care about who replaced Hammann II, another US Destroyer no one will use. Now take away the built in fan base....
Type-II ships are design to deal with the problem, instead of assigning a random name to a Nameless Yard Number, we take an existing name with an existing Fan Base. No one cares about Japanese Ship #5002 [Unryuu Class], she has no name and no history. Making up a name won't help anything, unless she make a major splash, she'll just disappear.
Take a Japanese Carrier, we'll use Shouhou because of Hiryuu META's presence and how it ties to Souryuu META, and use her with Hull #5002 for Shouhou II....and we have a ship that instantly has name recognition and has a fan base. While she may never be as popular as many other ships, she at least has a foundation that ships like Adalbert and Suruga never had to build from.
And it's not a long leap from using it with Yard Numbers to re-releasing ships as themselves. And it'll happen in a natural transition, probably with a Kongou-Class....who all happened to get prominent roles in the last Sakura Event. Instead of Kongou BB, she'll be Kongou II, and it'll be used to gauge reception.