Why is so much of the early game decided by what side of the map you start on?

Some examples Top lane: If I start bottom-left side of the map, I find I generally have a MUCH easier time avoiding ganks because I only really need to worry about warding the river bush, with the tri-bush really just being optional. On top-right side of the map though, ganks become much more of a problem

Jg: A single-target focused champ is going to want to start top-right side so that he gets both the double leash and the easier single target monsters. Aoe jungler will want to start bottom-left side for the AOE camps. Neither of these have any control which side they get.

Personal Mordekaiser thing: In top lane, if I'm low on top-right side, I can get a nice double heal off Krugs (and tons of farm). Bottom-left side, I can only get a single heal and (I think, not quite sure) less farm with Gromp.

There's a lot more minor stuff that I didn't bring up, like how your starting side can affect which lane you'll gank first, but I think you get the idea. It's not a huge issue by any means, but I think it's significant enough that it should be tweaked a bit. After all, just having bad luck on the side you start in isn't really fair.

I have heard this isn't really a problem in Dota 2. Now I don't know much about the game at all, so correct me if I'm wrong, but I think champions actually go in different lanes depending on which side of the map they start. Like: X champ goes top lane if he starts bottom-left side, and goes bot lane if he starts top-right side -- yet somehow, the lanes are the same for him no matter which side of the map he starts on. Like I said, I know next to nothing of Dota 2 or if there's anything else they do, but would this be at all feasible for LoL?