Can we route read-only connection to readable secondary replica without setting connection string (ApplicationIntent = ReadOnly)?
You would be required to set the Secondary Replica Copy as Readable, different from Read-Intent, and point the connection string to the actual instance where the replica resides.
This is not advisable, as it negates the HA usability of any Read-Intent replicas during failover.
No, you cannot route read-only connection request to readable-secondary without ApplicationIntent=ReadOnly connection parameter.
However, you can connect to readable secondary directly without using listener, but as it is mentioned on the other answer, in case the secondary replica is down, HA is not achievable, in this case.
I could not think of any such specific use case. I hope it helps!
For configuring read-only routing, check this page. Thanks!