I agree with your overall position, but think you're mischaracterizing Richards' tennis career a bit.
As Richard Raskin, Richards in the 1950s was a star HS athlete and BMOC at the prestigious male-only Horace Mann School in the Bronx, excelling on the tennis, swim, football and baseball teams. Richards excelled in football as a wide receiver and as an ace pitcher in baseball. Richards' baseball skills were so exceptional that the youngster was offered a position with the New York Yankees. But as someone who was academically gifted, and whose father was a professor at Columbia, Richards wanted a higher education and so went as an undergrad to Yale, which at the time only admitted men as undergraduates. At Yale, Richards was captain of the (men's) tennis team, and was considered by many to be one of the best men's college tennis players in the country.
After graduating from Yale, Richards went to the University of Rochester Medical Center, specializing in ophthalmology and graduating with an MD 1959. After a two-year internship and another two years of residency at hospitals in New York, Richards joined the United States Navy to continue medical training and to play (men's) tennis for the Navy, going on to win in both singles and doubles at the All Navy Championship.
After the Navy, Richards took a break from medicine for a few years to play competitive tennis for a while. When Richards married model Barbara Mole in June 1970, Richards was ranked sixth amongst American male tennis players over 35. (Mole and Richards had a son Nicholas in 1972. The couple divorced in 1975, the same year Richards had what at the time was called "male to female sex change surgery" and switched names from Richard Raskin to Renee Clark.)
Also, Richards didn't switch to playing women's tennis as seamlessly as you make it seem. In 1976, Richards played women's tennis in California in regional competitions for the John Wayne Tennis Club under the name Renee Clark. That summer, Richards as Clark entered the La Jolla Tennis Tournament Championships, crushing the competition. Due to Richards' distinctive left-hand serve - remarkably powerful for a woman - Richards-Clark was recognized by Bob Perry, a tour player who remembered Richard Raskin from the men's tennis circuit and joined the dots. The word began to spread.
Also in the summer of 1976, Richards was invited by a longtime male friend to play in the women's category at a professional tennis tournament in NJ called Tennis Week Open that the friend was in charge of. In protest, 25 of the 32 women competing withdrew; and the US Tennis Association and Women's Tennis Association also revoked their sanctions for the event, and organized another tournament.
In the summer of 1976, Richards also applied to play in the women's category at the United States Open, Wimbledon and the Italian Open and was denied because Richards refused to take the Barr body test that all competitors in the female division were required to take in order to verify their sex. Richards responded by suing the USTA, which runs the US Open, in New York state court on the grounds that the USTA was in violation of NY laws prohibiting sex discrimination and protecting human rights - which were relevant because the US Open is played in NY. Richards argued that the USTA was committing unlawful sex discrimination and human rights violations by refusing to recognize Richards' "right to be a woman." There was considerable controversy at the time.
In 1977, the NY state judge hearing the case found in Richards's favor. He ruled: "This person is now a female" and said that requiring Richards to take a Barr body test to establish that Richards has female sex chromosomes was "grossly unfair, discriminatory and inequitable, and a violation of her rights." He further ruled that the USTA intentionally discriminated against Richards, and granted Richards an injunction against the USTA and the US Open Committee, forcing them to allow Richards to play in the 1977 US Open.
At the 1977 US Open, Richards - by now 44 - lost to in the first round of the singles competition to British player Virginia Wade, who at age 32 was a dozen years younger. However, Richards made it to the finals in women's doubles in 1977. Richards retired from women's professional tennis in 1981.
Given that as a high school baseball pitcher, Richards had an impressive enough arm to be scouted and offered a position with the NY Yankees, I think Richards is correct in now saying that female pro tennis players wouldn't have stood a chance if Richards had decided to take up women's tennis in Richards' late teens- early 20s rather than waiting until Richards was already well into middle age.