Chest X-rays are commonly done for a wide range of chest symptoms and complaints. They are good at imaging the lungs, the mediastinum and bones of the chest. They have been done for many decades so that we have a lot of experience with them. Lung cancer is a killer and detecting it early is critical for best outcome. There are lung cancer screening programs but these involve CT.
A chest X-ray is a good start. It will often pick up big or significant abnormalities. It is not so good at picking up small things like nodules which represent early lung cancer. These cancers can be a centimeter or smaller. These are often not found on chest X-ray. These are best found on a CT.
The problem with X-ray is that there are many overlapping structures on an X-ray. You have blood vessels, bones, lung and soft tissues that the X-rays travel through to produce an image. These structures can obscure a small cancer or even produce the false appearance of one. The level of detail on a chest X-ray is also limited compared to a CT.
The X-ray also requires a high level of skill from the radiology doctor. Lung cancer can be very subtle on a chest X-ray. It can barely be seen or not at all. Sometimes you have to know where to look to really see it. X-ray training and experience in residency is not as extensive as in years past, like before CT became available.
While many big cancers that are say 3 centimeters or larger are identified, some of these can still hide on a chest X-ray. They may be positioned in the lower lung that overlaps with the diaphragm. They can be in the highest portion of the chest where there are many overlapping structures which can hide it. Some lung cancers are very faint and tough to appreciate.
I would say chest X-rays are a great and quick way to evaluate the chest. But it has to be remembered that chest X-rays will not identify many abnormalities, including big or major ones. If there is suspicion for a chest condition than CT is the best for that. Sometimes after a chest CT is done, you can go back to the chest X-ray and identify the abnormality retrospectively. Radiologists are human and as such, our perception is not perfect!