The original purpose of the overhead join was to allow either non-radio aircraft, or aircraft arriving at a non radio airfield, to overfly the airfield at a safe height, to observe the signal square, determine the runway in use and circuit direction, and then descend into the circuit pattern. To do this you must arrive in the overhead at 2000 ft; descending on the Deadside as you approach is as stated, a crosswind join.
Whilst I find most pilots understand the pattern, the choice of speeds and power settings leaves something to be desired; many glide down at glide speed (best suited for range!) often leaving the ATZ; only to rejoin on an unannounced crosswind leg. A few weeks ago I joined overhead at an airfield where I heard two other aircraft report Deadside Descending ahead of me; I was crossing the centreline and could see no other aircraft, I called, descended and was well established Downwind before the other two aircraft appeared on a crosswind leg about a mile behind me. Nobody watching would have had a clue what they were doing.