Multi-hash blockchains can be a great way for storing reduced information on the chain and providing solutions for lower security blockchain solutions. There migh be a catch however, state is not necessarily stored 100% percent at each block, there might be other strategies as well. As an example, there might be an option to store only the last couple of states, because based on the transactions and initial states the new states can be calculated or reinitialized. Another option might be to store the state redundant between blocks especially regarding parts that did not change, like on the following picture:
At any case, if the hash pointer is reinitialized, it means indirectly that the old blocks and state information might be deleted without effecting the consistency of the chain. As a consequence, there should not remain any dependency regarding the old blocks or the old chain. It implies that in such situation the state tree should be built up again without external dependencies. As the state is validated by the old state and the transactions, the exact storage of the state information should be irrelevant to the consensus mechanism, it just requires more space at hash pointer resets.