An ObjectID is a unique, not null integer field used to uniquely identify rows in tables in a geodatabase. ObjectIDs are limited to 32-bit values, which store a maximum value of 2,147,483,647.
So this satisfies the requirement for an ObjectID atleast.
Yes, they may not be the same and hence the question could be "Why does ArcGIS create a Primary Key in case of Feature Classes, but a Unique Index in case of Geodatabase Tables?"
From a quick test, it seems the behaviour is not same in an Oracle Enterprise gdb.
A Feature Class created in an Oracle sde gdb, does not have the ObjectID as a Primary Key.
I just ran into this issue... oddly it appears to be different if the database is 'geodatabase enabled' or not ... at least on SQL Server. I just created a table via ArcCatalog on a plain/non-geodatabase database connection and the OBJECTID column is set as the primary key by default.