If it were up to me...
You need to satisfy the requirements of the database and of your applications.
Adding an auto-incrementing integer or long id column to every table to serve as the primary key takes care of the database requirements.
You would then add at least one other unique index to the table for use by your application. This would be the index on employee_id, or account_id, or customer_id, etc. If possible, this index should not be a composite index.
I would favor indices on several fields individually over composite indices. The database will use the single field indices whenever the where clause includes those fields, but it will only use a composite when you provide the fields in exactly the correct order - meaning it can't use the second field in a composite index unless you provide both the first and second in your where clause.
I am all for using calculated or Function type indices - and would recommend using them over composite indices. It makes it very easy to use the function index by using the same function in your where clause.
This takes care of your application requirements.
It is highly likely that other non-primary indices are actually mappings of that indexes key value to a primary key value, not rowid()'s. This allows for physical sorting operations and deletes to occur without having to recreate these indices.