Not the 738, but we had a Technical Pilot on staff who did post maintenance test flights. The schedule he had developed called for a shut down and relight. After several cases where damage occurred during the relight process it was decided that this was no longer a good idea.
As Barking mad says, modern turbofan engines don't normally run down. So, unless the emergency dictates a relight, why do it? A modern aircraft has enough redundancy to get you home with one engine inoperative.
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.