Exercising a safety precaution every time versus verifying whether it is required

Cost of precaution: 100
Cost of verification: 101

Doing the precaution indiscriminately: 100

Verify, precaution needed: 201 (more than twice as inefficient)
Verify, precaution NOT needed: 101 (still less efficient)
Verify, error in verification, precaution not needed but done anyway: 201 + cost of embarrassment of failure (including loss of goodwill+trust of client or other party)
Verify, error in verification, precaution needed but not done: 101 + cost of whatever clusterfuck the precaution was designed to avoid

Factors to consider:
V Cost of verification
P Cost of precaution
N Chance that the precaution is needed
F Cost of failure of precaution when needed

If F itself implies ruin, then always go with the precaution and no other calculations matter: ignore the below.
The average cost of failure is F/N.
Our main 3 factors are then P, V and F/N.
If P is the smallest, then always go with the precaution.
If F/N is the smallest, then never go with the precaution.
It is only worth verifying if V is the smallest.

In this we are assuming:
This situation will play out enough times that F/N is meaningful.
Verification is not infallible.
When we say "smallest", the margin by which it is smallest exceeds the chance of the verification giving false comfort.

Of course, usually the work in doing the verification right significantly overlaps with the precaution itself (and sometimes the precaution is verifying something), minimizing the savings and leaving the temptation being to either say "fuck it" and skip both or doing a sloppy verification and increasing the risk of error.