Why don't all perseid meteors follow the same trajectory? Since these bits of debris crossing Earth's orbit have the same relative speed, why aren't they drawing parallel paths in the upper atmosphere? (consider one hour of observation to minimise Earth's rotation influence)
They are all following parallel paths. They are not on exactly the same trajectory but they are all travelling parallel to each to other in their orbit around the sun, in a stream of particles.

What you see is then multiple meteors on parallel paths. When you look in the direction that the meteors are coming from you see them appearing to radiate from a point

These meteors are all travelling parallel to each other. It is only perspective that makes them appear to be radiating from a point.



This is similar to the "flying through space" screensaver that used to be popular on windows.