I completely agree that psychological factors can block people going into a labour. In times of war, women will often not give birth during evacuations from their home or battles, until they have reached somewhere safe. Also stressed or scared women will often labour less effectively, hence why homebirths are so successful as women labour better at home where they feel comfortable and safe. However I would dispute this
I know that many women don't go into labour naturally
because all women will labour given enough time. Yes there are debates about how long is safe for a pregnancy to continue, but all women will eventually go into labour if left alone. In cases of induction, often babies are not in the right position to be born and therefore the induction is very likely to fail as the body will resist the process.

I would recommend you look into hypnobirthing or calmbirthing classes in preparation for your next labour as they will deal with the importance of having your mind prepared for labour as well as your body. Good luck