For example even if all of their useful functions will occur on the ETH blockchain, would a separate blockchain simplify the creation of DAPP tokens to trade on centralized exchanges?
The principal benefit having a private blockchain is that it's private.
Now would it be simpler to write, implement, deploy Dapps on a private blockchain ? absolutely not, it seems to me it would require the same efforts.
You'd lose also the benefits of having miners working for you and would have to endure the cost of running it.