As an emergency developed (ie, ship might go aground/lee shore approaching), all unnecessary crew would be taken off to minimise any possible loss of life (a ship that is completely abandoned becomes a derelict). The remaining crew would be the best seamen - captain, an officer, perhaps engineer and one or two crew.
As grounding becomes a probability, the anchors and chain should be run out to their fullest extent (all ships carry extensive lengths of chain) and made secure. Although this was a fully laden tanker, some 'drag' of the anchor and chains combined with experimentation of rudder angles could perhaps have altered the ship's 'attitude' and possibly controlled drift a little (a mile would have made all the difference).
Whether or not there is a tug, as the ship approaches the shallows - and even if the anchors don't 'hold' - drag and rudder can be used to advantage to achieve best attitude with the shore (eg, stern aground and bows out to sea).
This crew appear to have made no attempt to try to save their ship.
I noticed recently, when I went through the Dartford Tunnel, that HGVs carrying dangerous cargoes (eg, petrol tankers) are herded into special lay-bys and then taken through in convoy under escort. Need I say more?