Mostly this is because of WHY league has a meta in the first place, A lot of people know what leagues meta is, but not why it is
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As everyone knows League of Legends has Baron and Dragon, Baron at the top of the map and Dragon at the bottom.
Middle Lane is the shortest lane this means that champions that go to middle lane will level faster than either of the side lanes due to minions reaching them sooner, champions that are strong in the mid game are best in the mid lane so they can get that power spike and try to influence the game from there such as your assassins, it is also the safest lane due to no close in bushes, and it is the shortest lane, this means your immobile, strong in the mid game mages are good in the mid lane.
Top lane is far away from any early game objectives (Dragon) and it is a long lane so relatively unsafe for squishy champions that would be vulnerable to being ganked, so tanky champions generally go top lane, these are also the champions that have high impact in a team fight with CC and thus Teleport became Meta. Champs that are good top lane are ones that are strong with farm because it is so isolated that they can just farm and farm and farm, if the jungler comes up to gank that leaves Dragon open.
Bottom Lane has two champions because it gives increased protection around the early game Dragon objective, however in order to take advantage of all of Leagues resources effectively one of those champions needs to be someone that is good throughout the game without needing gold, (supports) and one of them needs to be able to have a late game influence, ADCs do extremely well with large amounts of gold, and are vulnerable in the early game, so they go bot with someone to protect them.
DOTA doesnt have the same style of objective control and gold resource management needs
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As for DOTA on the other hand you have the two sets of ancients in the jungle, (basically like old dragon) situated so they arent in the river and instead are each slightly towards either end of the map, which means that you dont need a particular set of champions in certain areas in order to guard them from enemies.
The jungle is not mirrored in DOTA either, they are shaped different for blue and red side, while red side has a better path for farming, blue side is better situated for ganking. However thats assuming you even have a jungler in the first place, the jungle is not a friendly place in DOTA, killing even the easiest of camps is impossible for most champs in DOTA at level one, and even the champions that are considered Junglers sometimes dont even start jungling until they've been in lane for 1-2 levels.
There are very few champions that actually have abilities that scale with items, and instead almost all abilities are base damage only. In dota there are three stats, and even if a champions main stat is intelligence, building intelligence items increases the damage of their auto attacks (as well as increasing their mana, agility increases attack speed and strength increases hp) This means that champion picks are not often influenced by items because you dont have to worry about any scaling, and choosing what item you want becomes purely about what sort of utility you want.
Abilities in DOTA cost a huge amount of mana compared to league, to the point where even the mages will only be able to cast all of their abilities 3 times before running out, so team comps are made around quick wombo combos instead of being able to plan for extended fights making nearly any champion viable in a certain team comp.
EDIT: Though take what I say about DOTA with a grain of salt, I dont like the game, it's way too luck based with almost every item giving your character some sort of luck stat so I stopped playing it a long time ago.
