For now, because the public chain doesn't have the privacy and scalability they need. They expect that to change, and which point they plan to migrate some applications to the public chain. In the meantime they're being careful to stay compatible, and contributing development resources. Also JP Morgan has a client that bridges public and private chains.
Source: I watched the EEA conference, and some smaller presentations later.
As far as I know the big corporations haven't invested in ETH. There are also some ICO-funded startups involved. I don't think the Ethereum Foundation is funding any private chain efforts, though they are collaborating with the EEA.
Them using the tech privately is seen as an indication of support (or at least interest) in the platform. So the public coin benefits from exposure and validation of its tech.
