There was a use of ASDA=TODA. Back in the '50s and '60s (and continuing into the '80s on V Bombers), when runway specific Regulated Take-Off Tables or Graphs (RTOTs or RTOGs) were not easily available for all the possible airfields at which you might end up and when MTOM calculations from scratch were tortuous it was common practice to carry generic RTOGs for fields at, for instance, zero, 1000ft PA and 2000ft PA. These were calculated on a balanced field TODA = ASDA for, perhaps, 8000ft, 9000ft and 10000ft.
If you found yourself in the back of beyond at 600ft PA with an ASDA of 9020ft and a TODA of 9300ft you could use the 9000ft balanced field graph for 1000ft PA and get some quick numbers that erred on the side of safety.
This is the historical reason why this definition is so common on this side of the pond but, as JT says, it is of little use to a modern pilot.