If mobs are not moving, then you are simply too far away. Mobs stop moving when the nearest player is more than 32 blocks away (the only exception to this is slimes, they will continue to bounce around in random directions)
Unless the design you are using has some provision to actively move the mobs into the kill area (water that can be cycled on & off and pistons being two common strategies), it relies on the mob wandering.
Since mobs will not spawn (due to dark; cage spawners work differently) within 24 blocks euclidean of a player, but (other than slimes) stop moving if more than 32 blocks euclidean from a player (a few seconds after spawning) the mob must enter the water (or other movement device) within this period or it will remain until it despawns (barring another sill moving mob 'nudging' it).
While placing open trap doors over the water may help (mob AI reads these as always closed), this inherent inefficiency is why active collection grinders are so popular.
If you're still at a point in the early game where an active collection is not practical (ie requires too many or unavailable resources), the best that can be done is to minimize the distance a mob would need to move before entering the collection streams… [Many 3x3 pads (the minimum size needed to spawn spiders) will result in fewer 'stuck' mobs than an equivalent number of spawning spaces in a few 8x8 pads.]
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WARNING: I have an extemely "grindy" playstyle; YMMV — if this doesn't seem fun to you, mine what you can from it & bin the rest.
As I understand it they need a 3X3 unobstructed space but only the center has to be a solid block.
text in wiki is still somewhat contradictory:
the quick reference says
"Light level of 7 or less, 3×3×2 space on solid blocks (spawns only on top of the central block). Top half of space may be occupied by transparent blocks (glass, etc.)."
whereas the body says
"Spiders spawn in the Overworld in 3×3×2 space on solid block(s) (they only need 1 solid block beneath) at a light level of 7 or less, in groups of 4. The top blocks can be transparent, but not solid."