Gridcoin would still serve as a currency when burnt. It would serve the typical role as a means to purchase goods, as well as a resource for organizations to be whitelisted. The whole burning idea is a way to counteract the inflationary nature of a unlimited coin.

So if a company spends X GRC to be whitelisted for a month, then X coins are being burnt from that transaction, which increases the price per GRC. If we were to set a price per month for whitelisting, lets say $100 worth of GRC for example, then the subsequent whitelisted companies would spend the same amount of USD, but less GRC each time do the increase in the price per GRC. So the amount of GRC burnt would lessen and lessen with every company added, and with every month of whitelisting paid for,while the price per GRC would rise.

With this we can keep the current work/reward system for GRC. The only thing that would need to be added is a way for companies to apply for whitelisting, and a way for the blockchain to be able to burn the GRC from said company.

Then again, I'm kinda new to all this and i'm just throwing some ideas out there that I had. I bet there's plenty of problems with this idea, but I'm always trying to help out and learn in the process.