Climbing on downwind minimises the variability of position compared to only turning once at circuit altitude. It's a lot easier to find an a/c that is constrained within a small area laterally ( ~ 'standard' circuit width) and maybe several hundred feet vertically up to ciruit height, than it is to find an a/c that could be anywhere within several nm. spacing.
To borrow H&T's paragraph
: the reason for this becomes very apparent particularly after having flown at some rather 'uncontrolled' airfields where joining procedure seems to be anything at any height.
For those who advocate variable width/constant height d-wind as a separation issue, how do you cope with low-level circuit traffic, or other types eg turbine, that may use 1500'?