In many aircraft the standbys are there not just for the posibility of a failure in the main indicating systems but also to cope with the possible situation of total power failure, fire etc i.e. where possibly the crew shut all the main systems down to conserve power. For example it is not much use having 3 IRS, 3 ADCs etc etc working perfectly if all the screens are blank!!
The QRH will have the definitive pointers as to what should be done. Many issues also apply - weather, time of day, aircraft current status etc.
What I would compare it to is imagine during the cruise you discovered that all the fire extinguishers were empty except the one under your seat. There is no sign of fire......but what do you do if one starts?
If you can remove the posibility of ever needing the standby eg remaining in VMC then no problem.
There are now aircraft certified with no standby wet compass. However, they have a separate independent flux detector and indicating system for heading on the standby.
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The good old magnetic compass can be used as a last resort to provide wings level information in places where dip is obvious.
It is most noticeable on a heading of North or South because on these headings if the aircraft is banked the compass will swing even if the heading remains constant. On headings of east or west it will not work.
The reason why in the northern hemisphere "South" is the preferred heading for such a let-down is because when on a heading of South if the aircraft is banked left the compass will indicate an apparrent left turn. This makes it less likely to cause confusion.
On a heading of North when the aircraft is banked left, the compass indicates an apparrent right turn. Can be confusing but I am sure that one could cope if there were mountains to the south!!
On the (magnetic) equator - it isn't going to work so simply resort to the simple = trim out wings level in a slow descent and let go = rely on the aircraft's stability.
or, if cloud base permits-
Enter a sipn in your favourite direction and hold it until you break cloud then recover. Not much chance of overspeeding in IMC there!!
Usual disclaimers about aircraft approved for spinning etc etc etc
