The reason the support typically goes bottom lane with another person who farms the lane is a matter of what constitutes an effective lane-phase strategy. Typically the bot lane farmer (usually a marksman, but doesn't actually have to be a marksman) is a champion with strong scaling with itemization, and the support usually has a strong early game and synergy with nearby allies. Most of the (champion) xp and gold you earn over the course of a game of LoL is earned from minions and/or monsters, as such, it is wise to spend most of your time, especially earlier on, in the presence of enemy minions or killing monsters (enemy minions grant xp as long as you're near them when they die, but jungle monsters only grant xp to their killer). The jungle only provides enough monsters to fully support 1 champion, and since xp is only granted for kills, you wouldn't get xp being in the jungle if you aren't the one killing the monsters, so the jungle position can only realistically support 1 champion per team.
That leaves 4 other champions and 3 lanes.
Because minion xp/champ is lower the more champs in a lane, and because no xp is given to anyone on your team for enemy minion deaths that aren't near one of your team's champions, the natural optimization to max xp and gold gained is to have a 1-1-2 split, with one lane having 2 champions and the others one each. So then the question becomes who should pair up and duo a lane, and which lane should be duoed?
The answer basically comes down to:
-Who suffers the least from getting less xp?
-Who has the best synergy with teammates?
Marksman aren't significantly affected by being behind in xp because most of their power comes from basic attacks which primarily scale with itemization, and supports are generally the most synergistic with teammates. The support not farming minions is advantageous because support kits typically are effective even without much if any stats to back them up, utility scales with CDR and not really anything else, and the other bot laner is usually a champion with strong itemization scaling, hence your team is, overall, stronger when the other bot laner gets as much of the gold as is practical.
So why is the duo usually bot? This is partly historical, before Rift Herald was invented, Baron was the only objective on top side of the map, and it didn't even spawn until 25 minutes in (lowered to 20 a long time ago, but in the beginning it was 25), hence the only important neutral objective was on the bottom side of the map, hence it was advantageous to have the duo in bot lane so that up to 4 of your team's champions were near enough to respond quickly to that objective, so the need or opportunity arise. It's only been with the rework that Rift Herald has become as impactful as first Dragon (the stats show about a 70% win rate for the team that takes either of them first), but a while earlier. Many pro teams had opted into the lane-swap meta as a way of accelerating the game and avoiding a potentially bad 2v2 lane matchup. This style of play was allowed for several season, and the NA in particular became famous for using it in most of their games. Riot eventually decided that it would be better for the game to have a further incentive to run standard lanes (it's a long discussion to examine all of the whys and hows), and made top tower have resistance to champion damage early on in the game, but bot tower does not. This asymmetry is the main reason standard lanes prevail in pro play today, as it's generally regarded as no longer worthwhile to swap your duo lane to top lane, as you are liable to lose first tower before the team that didn't swap.
Putting all of that together, it becomes pretty clear why the meta is what it is: Most of it is just good strategy, and there aren't many ways to innovate on most of it. (Some things, such as who goes bot to farm, and such have room for some innovation, but most of it is pretty decidedly better than the alternatives).
