The reason it wouldn’t collide has something to do with an element of the network of pipes that I haven’t mentioned yet.

First, all pipes have a pitch or slope. That’s to ensure that the flow only goes in one direction. Secondly, pipe joints have a “sweep” to them, meaning the joint directs the the waste to go in a certain direction when intersecting another pipe.

The fitting in the image below is called a sanitary wye(Y). Imagine that your toilet or sink would be the source of the waste and would be connected to the 2” side. You can see which direction this would direct the waste and each connection to the trunk would be directing the waste in the same direction. For this reason, your flush would never collide with another, instead it would be like you both would be speeding along in the same direction and just kind of blend together if they happened to meet in the pipe at any time.

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Pressurized plumbing does not have these sanitary features, they just have hard angles with no sweeps because the pressure is what pushes the water to your faucet. Drain lines lack this force so everything is handled by pitch and flow guidance in the form of these joints.