Now if the QRH specifically says to attempt a relight - as in a volcanic ash encounter - that is exactly what one should do.
But if the QRH is silent on the subject, leave it be.
There are operators who have tailored the QRH to suit their SOP's; and one such, approved by Boeing, is an simple ENG Failure with no indications of damage WILL be followed by an attempted inflight start. It's a crew decision in standard Boeing; there it is an SOP.