Generally, when folks say "x character has a good double jump" they actually mean "look at this cool thing x character can do with his double jump". For example, Ganon's double jump is good because he can NIL off the ledge for 18 frames of GALINT. Mewtwo's is amazing because it allows him to recover from anywhere. Fastfallers have great double jumps that they can use to mixup their aerial timings in neutral. DJC characters can throw out fast aerials and even amongst them you have characters that can DJL and those who don't want to DJL. The list goes on and on.
Eh IDK about this, in general 95% percent of the time when someone does say "x character has a good double jump" it refers to the speed and height of the jump.
It allows them to connect more vertical combos, usually means better ledge/platform options, and disallows being platform camped.
I agree that the unique aspects can obviously make some DJs better than others but in general when I hear talk of a DJ being good or excellent it's almost always for it's speed and/or height (e.g. Falco, Fox, Sheik, etc).