This idea of recommending one weight, and one weight only, of engine oil is strictly a rule of the EPA. The manufacturers have to recommend that weight oil that the manufacturer used to obtain their official mpg figures on the window sticker.
A look at an owner's manual from a vehicle I owned back in the 80's, a Pontiac Bonneville, show's recommendations for almost every weight of oil then manufactured, from straight 10 weight to 20W50, and everything in between. Temperature limitations applied. 20W50 was good from 20 degrees on up. 10W30 and 10W40 was good from 0 degrees on up. Straight 10 weight was good up to 60 degrees. Straight 30 weight was good above 40 degrees. The preferred viscosity was 10W30.