Re-submitted under new user id. Sorry.
If the trap stops the fumes why do you need to vent drains? Will they run slow? Why? It's not like a vacumn is forming in the line. I know it's the code but why?

The fumes need to go somewhere. The trap stops them from coming up through the sink, but they still need an outlet.

Turn a coke bottle upside down and pour. If it does not get air it does not drain well. You do not want that situation in your house.

There is only one way to prevent sewer gas fron escaping from a local vent that terminates inside a wall. This is a mechanical vent that is spring loaded so that it lets air in to vent but stops sewer gas from getting out. This vent is called a Studor Vent. A plumbing drainage system has traps on each fixture. These traps keep sewer gas from escaping into your house. On a unvented system the water draining sets up a suction that syphons the water out of the trap letting sewer gas out into your house. I have tried to explain how vents work and the different kinds. You asked how important venting is. Vents are necessary for a plumbing system to function. Cheers, Tom

A vacuum does form and it can siphon water from the trap if not vented properly.