Karl Wust and Arthur Gervais from Department of Computer Science of ETH Zurich point following factors that make public blockchain relevant in their paper “Do you need Blockchain?”.
1) A need to store state
2) There are multiple authors involved
3) Online trusted third party cannot be used always
4) All writers are known
5) Not all writers are trusted
6) Public verifiability is required
The scheme developed by these scientists is very applied. You can also use it to determine whether a private blockchain is needed or a project does not need this technology at all.