I'm skeptical such a situation can ever be stable. People have no incentive to create a transaction that will remain stuck in the backlog forever, regardless of the effect it may have on the rest of the system.

If someone invents a business model in which lots of payments are made, with fees, but that only clear probabilistically, perhaps such a situation could occur. But otherwise I think we have to assume that people won't make transactions that will lose the competition game, and instant demand would only ever be roughly equal to supply.