I suppose that the overhead join is a protocol, developed in the days of non radio aircraft, pre navaids, with the aim of joining in the most efficient manner.
As such is has beceome "best practice" (I do hate the term) and stuck around for a long time.
Personally, I've never much liked the overhead join, as overflying the signals square wasn't much of a need and with radio nav and GPS, airfield identification is not so challenging. So adding in a steep descent into an area of potentially higher traffic doesn't appeal to me, as we all kow that it is often harder to see other aircraft at a lower level due to ground clutter effect. And flying a low wing aeroplane type adds some blind spots too.
On the other hand, there have been few middairs in the circuit and the one I can think of involved a non standard circuit being flow by one aircraft (although the standard procedure was not an overhead join.)
So, being in mind TMM's experience, a question to ponder:
Is it time to develop some type of downwind join protocol, reducing confliction between departing and joining traffic?