Certainly not tied to any one Type. The AEO/OEI climb requirements are tied up with the certification philosophy and history .. the original explanatory words would be lost deep in the bowels of CAR 4b, I guess. Certainly, the basics haven't changed all that much in a long time. I probably have some earlier versions gathering dust in a filing cabinet somewhere but
CAR 4b.119(b) and 120(d) is the earliest electronic version I can find - at 1953.
More practically, a requirement which might impose OEI capability in the landing configuration would mean we could all retire and go fishing as the payloads wouldn't impress the beancounters ...
At the end of the day, the various Design Standard climb requirements provide lines in the sand so that the aircraft on the line is reasonably likely to have a chance of getting away from the ground at whichever maximum weight is relevant to the circumstances.
(I shall consider myself ticked off for indulging in wilful and gratuitous thread creep ....)