A good analogy is a queue. Imagine a society of mostly-identical people. You set up a stand that offers free sandwiches, but you can only give the sandwich to one person a minute. What will happen? A line will form outside your stand, growing longer until the length of the line is such that the discomfort of waiting in line is equal to the pleasure of eating the sandwich. So even though your sandwiches are supposedly free, a cost is still imposed on everyone who wants one, because they have to waste time standing in line.

You're right that people who can defer traveling to avoid traffic jams and congestion already tend to do so. But there are still people at the margin. People who don't value their time or don't mind sitting in traffic listening to the radio or dislike taking the bus. These people are creating congestion, imposting a cost on everyone else, and paying nothing for it. They would do it less if they had to pay. (It's okay for people to drive and sit in traffic, there's just no reason it should be free!) So it would really be more like "Good news! Surge pricing is in effect, and today your commute will cost you twice the usual price but take half as long!"