There are at least two problems with this. One is that it's not clear that it actually does anything for the environment. The process of building a new car creates pollution and uses energy and scarce resources; continuing to drive an old car does not. It may take years for the reduced emissions from a newer car to counteract the environmental cost of building a new car.
My second objective is that there is a better way--a way to get people to get rid their older cars when appropriate, that is, when the reduced emissions from the newer car are actually worth it: raise the price of gasoline via a tax. This will cause some people--those who drive the most--to switch to newer cars with improved fuel efficiency. Because these are the people who drive the most, the environmental payoff is likely to occur sooner (because the older, dirtier car would create more emissions over a given time period). This differs from the current cash for clunkers program, which encourages everyone with a vehicle meeting the requirements to buy a new car. A higher gasoline tax will also have other affects: It will encourage people to drive less by carpooling, combining trips, or taking alternative forms of transportation. It will encourage people to move out of rural areas, where a great deal of driving is necessary, to urban areas, where distances are shorter and alternatives to driving are more attractive.
It would be possible, with appropriate policies, to get these results in other ways than a gasoline tax. The government could mandate carpooling on certain days, issue limited licenses for cars in rural areas, or just force people to move. What if, however, some people have a lower cost of taking these actions than others? Don't we want the guy who lives in the country but has a lot of friends and contacts in the city to move their first, rather than the guy whose entire lifestyle is structured around country living? Don't we want to have the guy who drives a large SUV by himself to work every day to carpool, rather than the guy in his two-seat roadster?
In other words, it makes a lot more sense to use the price system and its system of incentives than to try to micromanage the various ways to get around, because people will tend to choose the optimal outcomes--it is in their interest to do so. Raising the gasoline tax causes people to find the low-hanging fruit on their own, rather than requiring the government to be clever and honest enough to catalogue all the fruit in the country and then send out bureaucrats to pick the low-hanging ones.