Spiders (and some other mobs) are not affected by speed effects or movementSpeed attributes

Spiders only become faster when they have a speed potion effect or a raised "movementSpeed" attribute. Even when they should be extremely fast, they remain similar to a normal spider speed.

To recreate, put this command into a command block:

/summon Spider ~ ~2 ~ {ActiveEffects:[{Amplifier:80,Id:1,Duration:199999980}],Attributes:[{Name:generic.movementSpeed,Base:3000.0}]}

The spider summoned will not be much faster than a normal one. To prove that it should be, you can try the same command with a zombie instead of a spider, and you will see that it moves extremely fast:

/summon Zombie ~ ~2 ~ {ActiveEffects:[{Amplifier:80,Id:1,Duration:199999980}],Attributes:[{Name:generic.movementSpeed,Base:3000.0}]}

UPDATE: This also doesn't work with Iron Golems, and I would guess many other mobs are not affected either.