WHM and AST should benefit more from spell speed (in theory) on a striking dummy. However, in raid, you are usually forced to break chain casts and clip GCDs to precast heal tank busters and raid AoE. This negates the GCD advantage you gain from spell speed. It is similar to how skill speed's benefit on NIN gets negated from using lengthy Mudras (especially 3 GCD Mudras like Suiton). Skill speed has always been thought of as a low priority stat on NIN.

On SCH, you could conceivably just Indom or Whispering Dawn for light raid damage and continue chain casting Broil. However, if you are required to precast a Succor (without Swiftcast) because your AST/WHM friend needs more AoE healing help, that is going to reduce the effectiveness of spell speed as well.

Most DPS jobs can benefit from speed since they are usually not forced to clip their GCD as often as healers.