FREDA, thanks but my question wasn't for you...
However, an aircraft calling "Downwind" is normally already in the circuit and should have made previous calls, giving other pilots a clue of their presence. I'm not advocating joining downwind as an alternative; but putting forward the disadvantage(s) of an overhead join as opposed to a deadside join.
Two aircraft can have and will continue to appear in the overhead at the same time, while the pilots are not concentrating fully on lookout, due to workload. Both pilots will be looking for the airfield and sorting out their orientation, particularly if they are not familiar with it.
When joining overhead there is no legal requirement to make a previous call. It's obviously good airmanship to call up for airfield details in advance, but many don't bother, or don't have a radio (the latter being the whole point of the procedure).
As you say, aircraft should be at the same circuit height on the downwind leg. Also, they should be in level flight, not one descending over another, in each other's blind spots, as required by an overhead join.
After seeing a few near misses at this (and other) aerial choke points, I prefer to think of alternatives.
The scenario I posted previously was one where we came extremely close to another aircraft joining in the overhead; the other nearly took our tail off from behind. We (I was not flying the aircraft) had called up with a position report for airfield details and announced our intention to make an overhead join. As my pilot flying called "Joining overhead", another aircraft also called the same, whilst almost hitting us from behind and above, and at a 90 degree angle to our track. He then cut across in front of us as he was descending more rapidly. There was no time for us to take avoiding action as he crossed behind us; we were a very few metres from a mid air collision. He hadn't seen us; he was manoeuvring in 3D whilst perhaps over-concentrating on his join procedure at the expense of looking out and not building situational awareness.
A 2D manoeuvre is, from my risk assessment and experience, less risky, in a high workload situation. The military obviously agree.