You know that no mobs will spawn within 24 blocks of a player?
Make up your mind, does nothing spawn or could they have spawned but be hanging around inside?
Don't ask us, just go take a look.
Assuming that nothing spawns and the platforms are far enough away, what steps have you taken to make sure the mobs don't have anywhere else to spawn?
Lighting up caves out to 128 blocks from where you will be standing for instance (and the surface if you want it to work at night).
What version are you playing?
1.14 and in particular some of the snapshots have had problems with mob spawning sometimes, some places and for some people.
Single player, on a server or Realms?
In multiplayer you need to take mobs spawning around other players into consideration.
Opening up the debug info, with "F3" usually, will show you the ingame entities (mostly mobs but also hopper, minecarts etc).
Look at the fifth line from the top, starting with an "E:", the first number is the number of entities within your field of view (not necessarily visible, they could be hidden, but in the direction you are looking) and the second number is how many there are in total. If the second number is 70 or more in single player then you probably have as many mobs in your world as you're going to and you need to find out where and what they are and stop them from spawning there if they're hostile mobs somewhere other than in your spawner.
Building your spawner more than 128 blocks above the surface may be easier than lighting up all the caves.
The mob cap in question is for hostile mobs specifically but the F3 info doesn't tell you what kind of entities it's detecting.
In plain vanilla Minecraft it's something like 0.2 hostile mobs per chunk within 8 chunks of a player, so the more spread out players are in multiplayer the more chunks will be used in the formula and the higher the mob cap will be, though typically the mobs will also be more spread out.
I believe that servers often have special rules for mob spawning, to limit lag or so, so it may vary.
If you only wanted the drops, not XP, then an alternative would be to build the spawner on or just below the surface and AFK 110 or so blocks up, then you wouldn't have as many caves to light and they'd be easier to find since you'd hear the mobs from the surface.
You could try using that method for an XP farm but since hostile mobs despawn over time if more than 32 blocks away you'd have to be going up and down like a yo-yo every few minutes or so.
Oh, yeah, most of this presupposes that you are in the right section of the forums, the Java edition section, otherwise the rules are somewhat different.
This just leads me further to want to abandon the mob spawner project
It just doesn't seem practical for large multiplayer map.
Mobs don't spawn if you're too close, they don't spawn if you're too far away, correct? At same time, there's limits to how many spawn so you have to compete with everywhere else....
I should instead find alternatives to the "Mob spawner"? Such as a skeleton spawner or zombie spawner?
The answer depends a good bit on what you want:
For Xp the upper end are ender enders (endermen farms built in the end dimension), guardian farms (built in the volume of an ocean monument), and zombie pigmen farms (generally built above the nether ceiling and as much for gold as Xp).
Lower efficiency (but easier to construct) options include general mob farms with active mob transport (instead of relying on mob wandering) or something as simple as an animal farm (note breeding gives more Xp than killing) or fishing hole.
As of 1.13, using furnaces to store Xp from smelting is also an option (eg a autofarm producing raw chicken can be used to feed a furnce fueled with the output of a charcoal generator and teh resulting Xp saved until needed).
For drops, you need to spawn the required mobs (eg creepers for gunpowder [as ghast farms tend to be large, difficult to construct, and inefficient]), and may need to actively kill them (rare drops like the zombie iron ingot occur only with player credited kills).
In either case…
for the design you appear to be describing, using smaller spawn platforms (note that spiders require at least 3x3 clear space) will lower the mean distance mobs must wander before falling into a water stream and/or lining the platforms with open trapdoors (which mob AI does not recognize as being open) will improve efficiency.
(Increasing the distance from the player to the spawn floors may also help as mobs will only begin to despawn after 30 seconds and only wander for a few seconds after spawning. Keeping spawned mobs above 32 distant will still capture most all of those that would otherwise have entered the collection system while lowering the mean time those that do not wait to despawn.)
For SMP play, if you are on the server alone, simple darkness based spawners work equivalently to SSP.
If another is also on, things get complex…
Because cage spawners ignore the mob cap when spawning (but the mobs spawned count against it), if another player is using a cage based farm, that player will receive a disproportionate percentage of the spawns.
Even if no others are using cage based farms, if the chunks being loaded by the other player is not well spawn proofed the majority of spawnable spaces will be near that player and will get the concominant percentage of the spawns.
Conversly, if the other player is in an area well spawn proofed, the overall mob cap will increase and the darkness spawner you build will see an increase in spawns.
Cooperative ventures can also be used, where farms of higher efficiecy (but greater cost) can be profitably shared by multiple players.
Of the three main types of naturally occuring overworld cage spawners (skeleton, spider, and zombie) skeleton spawners are generally most favored due to the utility of bone drops (and – to a much lesser extent – arrows), while zombie spawners are often least favored (the only common drop is rotten flesh which was often considered near useless even before 1.14 broke mass trading), with spider spawners intermediate (string can be crafted into wool and spider kockies provide small numbers of bones).
[Cave spider spawners can be easier to locate due to the frequency of mineshafts, but the smaller size makes player kill designs a bit more demanding; otherwise as stndard spider spawners.]
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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.
Even on multiplayer servers, a darkroom-based spawner that doesn't require the player to kill mobs (long drop and/or lava blade/magma-block/drowner kill methods) can generate a decent amount of common mob drops (gunpowder, bones, arrows, flesh, string) without having to spent long times AFK nearby IF you place them correctly. If they're near someplace you spend a lot of time anyways (main storage room, livestock pens, other farms, villager trading area, etc.) so they're beyond the 24 block no-spawn limit but not a whole lot farther than the 32-block mob-idle-mode limit, and DEFINITELY not past the 128-block immediate-despawn limit, you'll get at least some output whenever you're nearby. If you can wrap the rest of your base facilities around an underground darkroom grinder, even a fairly slow output will add up over time.
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