IIRC it depended on the design of the post. In all my bus spotting days I never did deduce a reason for the finials, it seemed to me (1960s) that they only appeared on older stops and either their function was redundant or that they were simply a feature of that stop design.
In my experience, many of the bus stops that were installed in the '50s were one piece reinforced concrete. That included the recess for the timetables. The post above the timetable area had a 'D' cross section and the flag was bolted through the concrete or sometimes held on with steel bands. The flag itself was about 3-4inches thick at the post end, tapering down to a curve of about 1inch radius at the other end. The post we as tapered towards the top then curved and just painted red instead of a finial.
On trolleybus routes, the pre-war iron posts carrying the wiring had framed enamel flags banded to them and no finial.
