Most companies with object based solutions have a mix of block/file/object storage chosen based on performance/cost reqs.
From a use case perspective:
Ultimately object storage was created to address unstructured data which is growing explosively, far quicker than structured data.
For example, if a database is structured data, unstructured would be a word doc or PDF.
How do you search 1 billion PDFs in a file system? (if it could even store that many in the first place).
How quickly could you search just the metadata of 1 billion files?
Object storage is currently used more for long term or archival, cheap and deep storage, that keeps track of more detail of what that data is. This metadata becomes very powerful when searching or mining very large data sets. Sometimes you can get what you need from the metadata without even accessing the data itself. Object storage solutions can typically replicate automatically with geographic failover built-in.
The problem is that application would have to be re-written to use object access methods rather than file hierarchy (which is simpler from a app dev perspective). It's really a change in the philosophy of data storage, and storing more actionable information about that data from a management standpoint as well as usage.
Quick example might be an MRI scan image. On Filesystem you have owner/creation date, but not much else. If it were an object, all of the information surrounding the MRI could be stored along with it in metadata, like patient name, MRI center location, the requesting Dr., insurance carrier, etc.
Block/file are more well suited for local access or OTLP where performance is more important than retention and cost.
For example, you would not want to wait minutes for a Word doc to open, but you could wait a few minutes for a data mining/business intelligence process to complete.
Another example would be a legal search where you have to search everything from 5 years ago to present. With retention policies in place to decrease the active data set and cost, how would you even do that without restoring from tape?
Object storage is a great solution for replacing long term archival methods like tape.
Setting up replication and failover for block and file can get very expensive in the enterprise and usually requires very expensive software and services.
Note: At the lower level, object storage access happens via the RESTful API which is more like a web request than accessing a file at the end of a path.