I can think of a number of reasons for wide circuits. Some justified, some not. Remember the circuit area is often defined as 3nm.
* A brand new circuit student needs more time to do things & a large circuit can help. Self limiting since as the students skill develops then smaller ciruits can progressively be flown. Similarly when converting someone onto a much faster or more complex type. There's a learning period while the poor sod's brain changes gear...
* Extending the circuit because of a slower a/c. Speed adjustment is preferable but may not be an option. So, given the choice, which leg to extend? I suggest upwind.
* Students taught to turn D/wind at 1000'. This I think is wrong. Different a/c will reach 1000' at different points. Even the same a/c will experience a changing positions due WAT effects so using altitude can't provide consistancy to spacing.
* Students taught to turn d/wind at 45deg (from the threshold or over their shoulder. Again, this won't be consistant. Presuming the 1st turn is at 500' (in Oz anyway. Not necessarily a requirement elsewhere in the world) then a/c performance will change when the x/wind turn is commenced ie how far upwind before turning. A 45deg initiated turn will then result in a variable spacing since one arm of the equilateral triangle will be variable, causing the second arm to vary. If 45deg relative to the a/c is used then the position changes according to whatever the drift allowance is.
* Students taught to turn base when the approach threshold is 45deg 'over their shoulder'. This isn't consistant - even with a constant d/wind spacing - since it changes with drift allowance.
I reckon the best(?) option is to turn x/wind when the rules & judgement allows, fly to what is visually the correct
spacing then turn d/wind irrespective of height or angle, then turn base at ~45 from the rwy threshold.
My two penneth.