That's not going to be the reason why it fails. If a compound has low binding affinity you can just use a higher % concentration to flood out the endogenous ligand. Take bicalutamide for example, yes the binding affinity is low, but at 50 mg daily it has no problem outcompeting testosterone and other androgens in the important areas of the body:
"The affinity of bicalutamide for the AR is relatively low as it is approximately 30 to 100 times lower than that of DHT , which is 2.5- to 10-fold as potent as an AR agonist as testosterone in bioassays and is the main endogenous ligand of the receptor in the prostate gland. ... However, typical clinical dosages of bicalutamide result in circulating levels of the drug that are thousands of times higher than those of testosterone and DHT, allowing it to powerfully prevent them from binding to and activating the receptor."
This is why CB is going to be used at high concentrations of 7.5% twice daily. Yes, it is probably not the strongest anti-androgen, but designing one that has all the properties we need (active in the skin but inactive in the rest of the body) is not that easy per se. If it's ineffective, it may just highlight the lack of efficacy of TOPICAL antiandrogens for Androgenetic Alopecia in general. After all, most things, Minoxidil included, seem to work much better orally.