When I was at university in Birmingham in the late 1980s I used to spend many a happy hour on the observation deck at BHX. Back then the ATP was in passenger service with British Midland and Manx. I saw it land on many occasions and it didn’t seem to have any more or less trouble with crosswinds than other types so I don’t think one can blame the aircraft here.
With regard to Discorde’s question, by the time the runways needed extending in the 1960s, 06/24 was hemmed in by the railway and the A45 so I am guessing extending 15/33 was a lot cheaper. In the late 1980s 06/24 was still in use with full length (4,600ft) available and the occasional BAC111 and B737-200 would land on it if winds were strong enough.