Then what is the use of One-Shot?
to generate profit for the aspirin manufacturers. The one-shot is a crutch developed in the olden days when logic (see solution below) was transistors and diodes. It, like e.g. malloc() for '51 C, was carried over to the modern technology becuase the traditionalists insisted on it.

In situations where I need a delayed pulse, what do I do?
my favorite is a shift register where you start by setting the input and the appropiate tap is your output, if you need a delayed pulse. If it is "pulse width you need, let the input set a flip flop and the output reset it.

Is cost not a consideration at all in any design? absolutely it is, but what is the value of a low cost design that does not work (reliably).

The design used here was suggested by another professional, who had used it succesfully in another context.
see above "traditionalists insisted"

Also, there are so called professionals that believe that testing proves something.

Erik