Though something like the duo bot is a result of the old design of the game creating a standard which is easier to stick to than to try other things which could yield better results.
You have that backwards. Duo bot isn't just a habit that formed because no one tried anything else. People tried everything else back in season 1, and duo bot is the most effective way to play the game.
ADCs scale better with items than levels, so sharing the xp but getting all the gold is fine. Top and mid are more level dependent, so they need the solo xp.
Supports aren't that dependent on items, so not getting gold isn't as big of a deal. And they offer a lot in their kit to help adcs get kills or escape ganks, thus getting them ahead in gold/preventing them from getting behind.
Mid is the shortest and hardest to gank lane, so a champion not having much mobility isn't a problem. Mid is also the easiest lane to roam from, and is in a good position to contest objectives or gank. They also tend to have wave clear to hold back sieges.
Top is a long lane, and there aren't many objectives near it, so sustain is good there.
JG needs to be able to gank and clear jg quickly