Your idea might work if you knew when and where the fire would be set. The image finding equipment could then be focused (it takes some time) and the data recorded. However the satellite can not record each and every section of land with great accuracy. The larger the section, the smaller the image.

To understand this, imagine you have a powerful telescope that can see a mouse one mile away. However there might only be a few visible mice in this area and to find one you might have to individually focus on millions of square feet of land. The odds are low that you will find the right one.

Keep in mind you are looking down from above with a satellite, assuming you could actually find the person and their car, you would get a great picture of their head and top of their car. FYI, number plates are mounted vertically. Not visible from above.

On a similar topic, a lot of brush fires get started by lightening strikes. Lightening strikes emit radio waves and you could use triangulation to find out the rough location of strikes and send someone to have a look to see if a fire had started because of the strike, you could then put it out early without needing the huge amount of resource when these fires really take hold.

Do arsonists carry mobile phones with them like most of the population? and can you get a signal out in the places where these brush fires start?. If the previous conditions are true then a good place for the police to start looking would be the cell phone companies records for that area around the time they think the fire was started, would provide a list of people in the location who could be questioned as to whether they witnessed the fire being started or who may actually be the arsonist.

Nabbing may not be possible but there can be appropriate software which can scan the satellite sent images to auto-detect the fire and raise an early alarm. Some of them could be false ones, but this overhead should be worth taking to be on the safer side.