It's important to keep in mind that in 1972 when the US Congress voted in Title IX, and Nixon signed it into law, the matter of how Title IX would impact school sports was unsettled - and a topic of controversy.
In the years leading up to the passage of Title IX in 1972, the main focus wasn’t on the fact that most schools in the US didn’t offer girls and women the chance to do school sports at all, and that the minority of schools which did offer sports programs for female students only provided girls and women with a couple of sport options - and tended to give women's and girls' sports programs paltry funding, inferior or absent facilities and equipment, little or subpar coaching, and hardly any institutional support.
In 1972, the major concern in the US was all the other kinds of sex discrimination against girls and women that long had been widespread in US education - such as higher admissions standards, and strict quotas limiting the number of female students admitted to graduate programs in fields like medicine, law, business, architecture and engineering.
It took more legislation from Congress, regulations from the executive branch, and a bunch of lawsuits and court decision over the course of the 1970s and 80s to clarify exactly what Title IX would mean for school sports.