Edit: For comparison, a chest X-ray is around 0.1mSv, a chest CT at 6.1mSv, so a factor of 61 between (https://www.radiologyinfo.org/en/info/safety-xray ). Compared to natural exposure (usually 1 to 3mSv/a) however, a chest CT isn't that bad at 2 to 3 years natural dose, 2 polar flights or 1 year of living at higher altitude or Ramsar (https://aerb.gov.in/images/PDF/image/34086353.pdf ). Acute one-time dose damage has been shown above 100mSv, below that there is no damage shown, only statistical extrapolations.
So I'd say that the risk of using a CT right away should be lower than the risk of overlooking a bleed or a clot in an emergency, where time is of the essence and the dance of "let's do an X-ray first..." might kill more patients than the cancers caused by those CTs.
https://en.wikipedia.org/wiki/Linear_no-threshold_model
Edit: For comparison, a chest X-ray is around 0.1mSv, a chest CT at 6.1mSv, so a factor of 61 between (https://www.radiologyinfo.org/en/info/safety-xray ). Compared to natural exposure (usually 1 to 3mSv/a) however, a chest CT isn't that bad at 2 to 3 years natural dose, 2 polar flights or 1 year of living at higher altitude or Ramsar (https://aerb.gov.in/images/PDF/image/34086353.pdf ). Acute one-time dose damage has been shown above 100mSv, below that there is no damage shown, only statistical extrapolations.
So I'd say that the risk of using a CT right away should be lower than the risk of overlooking a bleed or a clot in an emergency, where time is of the essence and the dance of "let's do an X-ray first..." might kill more patients than the cancers caused by those CTs.