You can have blockchains without decentralized consensus. It's how Certificate Transparency works.

You have the contract host record all operations and output on a ledger, and then ship that ledger/log out to monitors. This improves the auditability of the system, and enforces the backend logic as a contract. Deviations from the code are detectable by replay, and then provable. Flag the host and readjust your trust.

You can also find ways to reduce the cost of switching between traditional hosting models, such as using data-sharing networks (Dat, IPFS) to quickly "hydrate" a new host, and good ole configurable endpoints to make the switch.

It's the opposite of a trustless network; it's a trust network built on accountability. You watch hosts for bad behavior (such as the violation of the backend contract) and reconfigure trust around violations. No decentralized operation, but much less wasteful than PoW.