The length between the trap and the vent can be longer if the pipe is bigger.
Small pipe, means a shorter distance between the trap and vent.
The vent is to break the siphon effect and to prevent the water in the trap from running up and out, leaving an empty pipe, which can be very smelly.
Have you ever siphoned water before?
If you lift the hose out of the water for even a second, it quits siphoning.
The vent does that for you,
A siphon is bad, it pulls the water out.
So yes, a vent a little close is better at that.
You can run the max distance, but you are also at the end of what consistently works.
Consistent because the distance is based on a clean pipe.
A gooey, gunky pipe, reduces the effectiveness by decreasing the diameter of the inside pipe area. That is why cleaning and snaking a pipe helps when it has slimmy gooey stuff in it, that reminds me, Is it dinner yet?