but in a country that uses U.S. TERPS
Not overly familiar with TERPS and would defer to you on PANS/OPS as well, in any case, good sir.
AEO planned turns are not commonplace but, sometimes - due to terrain - are necessary.
For instance, Hobart 30 (AUS) has an early turn to avoid tiger country. It used to be SOP to do this for all 30 departures as the OEI escape followed this procedure. I imagine the present operators still do the same as the payload penalties running straight out would be uneconomic ..