Why the King tiger? Ostheer already has a heavy tank, the Tiger. And, The tiger Ace is already very similar to the king tiger, as it has spearhead.
If any one unit is going to be swapped with OKW, should it not be the Jagdpanzer IV? It would bring a lot more diversity to the table, Ostheer does not have a 60 range tank destroyer.
Tldr
Ostheer already has a heavy tank, so why add the KT
Ostheer does not have a 60 range TD, add the Jagdpanzer IV?
The OKW already had the King Tiger as well but they added the Tiger to it so why not? More faction diversity in what options you have, plus like I said it wouldn't be the same unit but a unique one with it's own new special abilities that are nowhere else to be found in Ostheer.
As far as a 60 range TD goes, then what is the Elefant/Ferdinand exactly?
But overall I agree with you on the Jagdpanzer IV, I just don't really know a lot about it, where it was deployed and so forth while with the KT there's the theme of the 503rd Heavy Tank Battalion being transferred with their King Tigers from Normandy over to the Eastern Front in Hungary and it fits with Mobile Defense in that regard at least of having OKW things be transferred over to Ost.
While the Tiger Ace is pretty much just a regular Tiger but with some more HP from what I know, starts at Vet 1, costs more and has Self-repair, can't upgrade to an MG and so forth. While a King Tiger would have a bit more armor, would be slower, somewhat the same price so again, they're not going to be the same unit and they're going to fit different strategies and tactics.
If you want to use a KT as a regular Tiger I mean good luck with that lol.
Tiger is more balanced in terms of speed, armor and armament while the KT is heavier and slower, like a fortress/bunker on tracks, again fitting the "Mobile" part of "Defense".
Edit:
Forgot to mention, the King Tiger could use the Tiger/generic heavy tank voices for the Ostheer similar to the OKW Tiger, not sure if it can be done for the Jagdpanzer IV in the same way.