Attacking/Casting while on the move

Why was the ability to attack and move at the same time never implemented into the game. Like In certain RTS, you move a character, and as long as they are within range of that character, they shoot/attack it. I'm not saying it be automatic, but why not have it key binded.

I am very well aware of shift+click. What that does though is reduce mouse clicking. Normally you would click the target, then click away, click the target, click away. This is how you would kite from an enemy. With attack+move via shift, now you only have to shift+click away to attack and move.

But, every time you attack, your champion stops, even if just briefly.

Is it because it would make adc's and other champs too broken, if they were able to shoot and kite away at the same time? I guess the same could be asked of spells, why not be able to move and cast at the same time? Maybe it is just a stupid question and would break the game or mechanics in some way, just curious that's all.