This is a straw man's argument. So because there's virtually no reports of women being raped by trans women, you assume it's because of the lack of reports of rape.

I could use the exact same argument aganst you. I purpose there are over 1000 rapes a year by people named Buffy. Is there any proofs? Well, rape is highly under reported, so there's no reason this is false. Therefore people named Buffy should be banned from women's restrooms due to the fact the rape over 1000 women a year.