It is not always necessary to develop a cryptocurrency to apply blockchain technology to perform a certain function.
An example of such is Hyperledger Fabric, which is a blockchain framework for enterprises and authorised participants.
As stated in its official documentation, Fabric is capable of using certain consensus algorithms that do not require a native cryptocurrency for rewarding miners and paying for executing smart contracts.
In other words, there are certain organizations running the platform following the established rules.
This approach may be suitable for business processes such as exchange of information between enterprises.
Thus, blockchain and cryptocurrency are two different concepts.
The removal of the native token, however, does not guarantee the success of a blockchain.
Security, consensus on transactions, governance, practical use cases, and sufficient participants to run a network are some of the factors that determine the success of a blockchain.
Permissionless blockchains have a unique problem as participants can be strangers, and therefore economic incentives through transaction fees are possible for securing the network from spammers.
An example is Ethereum, which requires fees in the native currency called ether.
It all comes down to the design and intentions of the blockchain.