Millions of births not officially recorded
Originally, I believed Floyda was registering her birth with the court so she could apply for a Social Security number. But then I read newspapers of the time and discovered that this wasn't the only reason for registering births years or decades after the fact.
In 1940, with Social Security in place and WWII draft registration in force, the question of how to prove name, birth place, and birth place was becoming more urgent. According to the Milwaukee Journal newspaper (Aug 13, 1941), some 60 million people had no legally-acceptable birth documents because they were born before the requirement to officially register births (and sometimes marriages and deaths) with county or state authorities.
In Ohio, where Floyda was born, probate judges were strongly urging the governor to act to provide a pathway to legally and smoothly register births and correct errors that may have been in the oldest records. According to the Toledo Blade newspaper (Thursday, Jul 18, 1940), about half of the old records in the state were incorrect. Names might have been wrong, dates wrong, even sex recorded incorrectly. Fixing the mistakes and registering births not on the books were priorities, but no standard process existed for doing so.
How to prove birth in Ohio
In 1941, the Ohio House unanimously passed a bill mandating that the state Department of Health set up a system for official filing of birth and death records in the state. The goal was to ease the way for draft registrants and applicants for defense jobs to prove who they were, according to the Wooster Daily Record newspaper (Feb 21, 1941). These registrations would also help in the event of veterans applying for benefits later in life.
By 1942, those without official birth documents were finding help in all kinds of places. Even the US Census Bureau was offering to search its records (for a small fee) and provide documentation of someone being enumerated in a specific place and time (according to the Columbus Evening Dispatch newspaper, Sep 15, 1942). The Census folks were also drawing on WWI draft registration cards as proof of name and birth date/place. An estimated 2.8 million Ohioans were in need of official birth proof at that point.
Floyda's birth is recorded 66 years late
Why Floyda needed or wanted an official birth document, I can't be sure. Her husband Brice Larimer McClure (1878-1970) worked in a defense industry firm and had proof of his own birth, so perhaps the employer(s) were checking that spouses and immediate family passed muster.
I can't find Floyda in the Social Security claims or death index. She did work during WWII, as a part-timer in a Cleveland department store, but it's unclear whether the store would have requested a Social Security card as part of her employment process.
Most likely Floyda simply wanted to register her birth because of the state's publicity campaign to get all births on the record. And so her older sisters stepped up with affidavits that enabled Floyda to have her birth filed with the state of Ohio 66 years after she was born at home in Nevada, Wyandot County.