The crucial question here, for the women who married alien couples, is when did the couples marry? Between 1907 and 1922, women who were US-born lost their US citizenship when marrying a foreign (aka "alien") husband.
For an overview of the complicated history of US Naturalization law as it pertains to women, see Women and Naturalization, ca. 1802–1940 by Marian L. Smith, Prologue magazine, Summer 1998, Vol. 30, No. 2 | Genealogy Notes (two part-article; the link to part 2 is a the bottom of part 1). The rough timeline below was extracted from this article.
Due to an Act in March 1907, US-born women who married aliens took on the citizenship of their husbands and lost their US Citizenship. This was the case until the Cable Act on September 22, 1922, after which time, women's naturalizion status did not depend on their husband's, and married women could apply for naturalization on their own behalf.
After 1936, women whose marriage had ended through death or divorce could repatriate simply by taking an Oath of Allegiance. In 1940, Congress removed the restriction and all women who lost their citizenship between 1907 and 1922, regardless of marital status could apply to repatriate, not just women who had been divorced or widowed.
From Petition Number: 112937 for Mrs. Mary Connelly, 29 Nov 1938 District Court, Western District, Pennsylvania, viewed via Ancestry's database Pennsylvania, Federal Naturalization Records, 1795-1931
Many of these applications may have taken place so the woman could receive some benefit, such as a job during World War 2 that required a person to be a citizen. Some women may not have realized that they had lost their citizenship through marriage until years later. During the decade after the Cable Act, it took time for everyone to catch up with the new laws so the forms can be confusing.
For the marriages where the husband was also US-born, I would check to see if the husband had done something which caused him to lose his own US citizenship, or if he belonged to a group that was racially ineligible to naturalize. Something must have caused the women to go through the process of naturalization, whether they needed to or not.
The current guidelines for non-citizens getting a Social Security Number are here: Social Security Numbers for Non-Citizens and Your Social Security Number and card. The latter document lists the following substitutes if you are US-born but do not have a US birth certificate:
- Religious record made before the age of 5 showing your date of birth; or
- US hospital record of your birth; or
The online history The Story of the Social Security Number says that "SSA began requiring proof of age, identity, and citizenship" in the 1970s."
To test your theory about whether Social Security benefits might be the sought-after benefit, try cross-checking against other record sets, such as Ancestry's Social Security Application and Claims Index and the US National Archives' Access to Archival Datbases (AAD) NUMIDENT database.
Check for delayed birth records (noting the application date), the date of the marriage to the alien spouse, and the date of death of the spouse or a divorce date.
For a general overview of US Naturalization, see the class United States Naturalization Records by Danielle Batson, AG, MLS, in the FamilySearch Learning Center. Both video & handout are available for download.