That will only happen if public transport improves in a massive way and even then people will still want the freedom that a car brings.
Not everyone lives within walking distance of town and not everyone lives a bus ride away from work.
The busiest times of the day on the roads are school run and morning work traffic, and school run and afternoon end or work day traffic. Stafford is not a big place, it very easy to cycle from one side to the other in approx 30 mins, 15 mins from the outer housing estates to town. If those that were able to cycle/walk or get public transport did, then their wouldn't be any traffic chaos. The problem is caused by local people doing short journeys that could quite easily be done by foot or bike.
During the day the bus service in Stafford is pretty decent, I'm not a fan, preferring to walk or cycle, but the frequency of the buses cannot be moaned about. it is expensive, but in comparison to running a car, not really that expensive. The evenings is more problematic, but there isn't a traffic problem in the evenings.
I know people who drive from Castlefields to the Hospital to work, I know people who drive from Sandon Rd to Tollgate Ind Est (about 100 yards in distance for pedestrians), I know people who drive from Parkside to Tollgate Ind Est, I know people who drive from Parkside to town. Why??? All of these people are physically able, quite able to cycle. It makes no sense. These same people then moan about the weight they have put on and then drive to Esporta/Virgin, whatever the hell it's called now. If they'd incorporated walking/cycling into their daily routine they could save on the gym bills, save on the petrol bills, help de-clog the roads, and get themselves healthier.
I'm not advocating banning cars, or stopping people driving when necessary, of course I'm not, but if a journey is less than 3 miles and around Stafford, why not walk or cycle. It's not as if the car is quicker because almost everyone at rush hours is going nowhere fast! And there would be massive benefits in health, the roads would be safer for kids, it would be quieter for everyone, think England in the 1960's
What's patently clear is that continuing to build roads is an Elastoplast on a broken bone type of solution - its doomed to fail.