Does blockchain without currency make any sense?
There are a number of research papers that cover the question &quot;Do you need a blockchain?&quot;, e.g. the eponymous paper by Wüst &amp; Gervais (2017) and the extensive Blockchain Technology Overview by NIST (2018). At a quick glance, the article When do you need blockchain? Decision models. by Meunier appears to provide a survey collecting a broad range of answers to the question.
The general gist seems to be that you only need a blockchain if all of the following conditions apply to your use case:

an actual business problem that needs solving
shared consistent state
multiple authors
append-only data
no sensitive information
participants do not agree on single trusted third party

Since blockchains are complex and wasteful, they usually are not a better solution to problems that can be solved building on trusted third parties, audits, and distributed databases. If one or multiple of the listed criteria are not met, your problem can likely be more easily solved using these well-explored approaches. Blockchains tend to be the best approach only when they are the only option.
Meunier concludes a bit tongue-in-cheek that the only convincing application so far is the creation of unregulated money.