I believe you're saying that under an assumption that corporations will adopt a form of blockchain that is already available on the market.
Not necessarily, no, but the technology will still be important.
[permissioned blockchains]
It is a entirely different paradigm of privacy. You still have blockchain, which is easily auditable and verifiable for any party that might have such rights, but a competitor would not be able to even connect to the blockchain.
The real world doesn't work that way. Business collaborate one day and compete the next (or even the very same day). Even when collaborating they don't want to share all information, and certainly not with every member of a group. To control access to information once access to the blockchain has been granted at all, privacy features are needed.
Permissioned blockchains will often need privacy, just as the current example (or maybe more near future, but I'm not sure of the deployment schedule) of the Liquid permissioned blockchain does. Depending on the nature of the use cases for the permissioned blockchains, there may be some exceptions (explicitly public records perhaps).
Furthermore, I'm not even sure there will be too many successful permissioned blockchains. In the past, there were many proprietary closed networks. A few still exist, but most communication now happens over the regular internet. Not even VPNs, but web services with access keys. The need for many interconnections may in time make these closed/semiclosed systems impractical and/or cost-ineffective even when the interaction takes the form of blockchains.