Time for a history lesson. When the game first came out, it was pretty chaotic, and you could play any champion in any role and be successful because few people had to knowledge required to counter pick. Then, as people started realising the value of farm, they started assigning themselves dedicated lanes to farm in. But oh no, there are more players than lanes, better have someone dedicated to farming the jungle so the team has more gold. And so the role of jungler developed.
But there were still 3 lanes and 4 players, so it was clear that there would not be enough income to sustain 4 carry champions, so someone would have to go without farm and try and help the team as much as possible without carrying by damage. And so the role of support developed.
Now which type of character would benefit most from having this support lane with them? Tanks don't need to be supported because they are more valuable for their utility. Mages can't be supported because splitting the exp would put them behind in lvls and therefore make their abilities do less dmg. However, marksmen are perfect candidates for being supported, because they rely predominantly on gold and not on levels, because they do most of their damage with autos. And so the support/ADC combo was developed. This duo lane was assigned bot lane because it is closest to dragon and therefore can have most impact on dragon fights.
The association with mid lane and high damage carries is simply because mid is (obviously) the central lane, so these carries can have most impact on the entire map. They also get a slight level advantage (which therefore makes their abilities do more damage) because the minions reach mid lane faster. And so the roles of carry midlaners developed.
Now look at top lane. Before herald, there was nothing of any importance on that side of the map, so you were unlikely to receive any help from your team due to the lost pressure on bot lane/dragon if the jungler was to come top. Therefore top laners need to be champions that are able to survive on their own with little assistance from their team. This means is was unreliable to play any carries top, because if you fell behind your team would be unable to help and you would be useless. It was therefore logical that top laners would be champions that do not require much gold to operate and would still be useful to their team (through utility/peel) if they fell behind. And so tanky and bruiser champions were played top.
I'm not entirely sure why I wrote all this out, but I guess I just wanted to demonstrate how the pros didn't just pick lane numbers out of a hat and decide to role with it. There is a reason this meta has existed for 5+ years and not seen any major changes, and that's because this meta is logical and optimal.