What type of pump/gearbox/bearings?
I think that some companies are archaic with fluid recommendations. I don't see any reason why a detergent oil can't be used. I believe the old way of thinking is that a non-detergent oil is straight weight and less shear prone. Most newer motor oils are pretty shear prone.
The only thing that I see that might not be good is the reduced level of certain additives in newer motor oils. The typical straight weight oils, and the race, HDEO, or motorcyle oils, don't always have EPA happy levels of AW/EP additives. The manufacturer recommendations might be assuming that most straight weight oils have a good ol' dose of ZDDP, or that non-detergent oils have more oil and less non-needed additives(like detergents, pour point depresents, viscosity index improvers...).
So, it comes down to the type of machinery, the loads that are present, the temperature that the oil typical runs at, and type of contamination. I wish that manufacturers would provide oil weight range and additive level recommendations, instead of just recommending certain oil types.