Where we fly you join over the numbers. The problem with joining at the far upwind end is the potential conflict with aircraft on climbout within the circuit.
An abreviated crosswind join is called a "midfield " crosswind, and leaves a shorter downwind leg.
New regulations in Australia allow joining the circuit on down wind or base, but its not really encouraged. Crossfield joins are still the recommended route. The overflight is minimum 500 ft, and in Australia the 1000 ft overflight with descent on the dead side is preferred.
One way to get caught out is if there is a high performance aircraft on a 1500 ft agl circuit without a straight in approach, or a sports aircraft sharing the field on a 500 ft agl slow close circuit.
Lots of variations to watch out for.