Also as one lonely planet (which is one of the most important references in traveling) says: Iran safer than Europe, which the link below can blow your mind against all the propaganda you may hear on your daily basis.
https://www.lonelyplanet.com/iran/safety

Between these countries, iran has been chosen for the women who want to travel alone in Iran. So this is why we have so many Female solo travelers in Iran. The reason behind such security is not only the military power of the Iran. It is also because of the old culture of Persians!

First of all, the Regime in Iran seeks to build an ideal moralistic society, after the revolution. This goal is Exactly the purpose and Main goal of the revolutionary regime in Iran. In this regime, the women are the core and most important part of the society and the families. Even the main reason behind all of the wars against America and the ideology of liberal democracy. The regime seeks to build an ideal moralistic society through the ideal moralistic mothers of future. So the virtuousness of women and men are the main goal, through the management of Physical relationships instead of prohibiting Physical Relationship like christianity or Physical Relationship without any rules like everywhere in today’s world. In Iran all of the people have a higher value for the Female, than the Male. And when the smallest thing happens for a woman, everybody summons to help her. This protection feeling for the women and everything else which has value for you is called “Gheyrat” feeling. Gheyrat feeling is a very deep in the nature of all of the humans in the world which philosophically means: “a feeling for protecting everything that has value for you”. Meaning if the virtuousness of your mother, wife or sister has value for you, you go to protect it. If you feel something as your honor or your dignity, you will protect it. Overall Gheyrat is a word which has a daily usage in Iran and you can hear it everyday in the society.

Secondly, Iran’s or Persia’s culture is heavily based on Moral and the highest feeling a human being can reach, in the aspect of spiritualism. Through ages, Persia has advanced in Literature and Philosophy. (So Persian language itself is an extremely powerful and simple language for the human based sciences) The Persian literature is full of moralistic guidance and moralistic challenges to make the best person possible out of yourself. Almost all of the poems in Persian are about the deepest human needs and deepest feelings a human can reach. So overall in Persia you should always be a role model for yourself and for your friends and most importantly for you own children! This is why in Iran you have a Ta’arof Culture, which is based on politeness. So in Persia, your guide should teach you about Ta’arof culture, which is very important for you to learn, so you can understands why you should Beg a person many times to accept a Tip from you!

We have taught the Ta’arof culture to you in the link below, in best version possible that you can find on the internet:
Thirdly there is Hospitality culture in Iran which is yet based on the principles of the moralistic society. When you visit Iran even as an American, they will welcome you heavily. And if they don’t hug you, it’s because it may sound crazy to foreigners . So although in Persia the people are against having Physical Relationship and marrying like the west world, they welcome you like that, because they have learned to be a role model. So through being a role model and the proper laws to protect from the moralistic values, the Persia’s culture and society is built. But foreigners and tourists can legally do whatever they want to do, but women should just wear a scarf to respect the society.
So this is why there is such an extreme safety in Iran especially for a Female Solo Traveler.