Is marrying more than one wife restricted to achieving justice regarding the wealth of female orphans, and has this reason become obsolete with the existence of social security, and is polygyny permissible for the purpose of chastity?

The notion that the verse (And if you fear that you will not deal justly with the orphan girls...) indicates that the purpose of polygyny is to care for orphans is a fallacious and weak argument. Aisha was asked about the verse, and she clarified that the orphan girl would be under the guardianship of her guardian, who would desire to marry her without giving her a just dowry. So Allah forbade them from doing so unless they dealt justly, and commanded them to marry what pleases them of other women. This means that the verse came to explain the ruling on marrying an orphan girl under guardianship, not for the purpose of polygyny for the sake of orphans. There is abundant evidence for the permissibility of polygyny for those who are able, including the Prophet's (peace be upon him) encouragement of marriage and increasing progeny, and his (peace be upon him) approval of his companions who were married to more than one woman, with the limit set at four free wives.