After a failed IVF cycle, should couples try to conceive naturally before the next cycle? Here the assumption is there is gap of 6 months

Yes. Yes try but why the gap of 6 months? Usually you should keep going because time is not a friend to the woman. A "wash out" month is usually all that is needed. If finances prevent continuing then see if you get lucky. Talk with your doc about options as they will know your situation. I hope this helps.
Couple preference. Should? Only if that's what the couple prefers. Most times it's personal rather than medical factors that make a couple delay, although medical considerations can sometimes make the decision. At age 38 6 months is not trivial, but likely not critical either.