If a non-trans-man pervert/rapist really did want to go into a ladies' loo, why would he bother applying for a certificate that would make no difference to his legal right to be there, and which no-one would ask to see?
That's not the point. Currently if I see a man in the women's toilets at Asda I can get the shop security staff to get him kicked out.
If it becomes the norm to see male bodied people in the female toilets because it's about identity now, and if you have a feminine identity you can use the women's toilets even if you are still indisputably male looking, it makes it easier for men with ill-intent to abuse the system. It makes it nearly impossible for women to identify them. It makes it impossible for business owners to identify who should really be using the women's loo's.
It's creating a system which is ripe for abuse, and riding rough-shod over the real and still valid reasons why women have single sex provision. You appear to believe no man would ever take advantage of the weaknesses in such a system. I don't consider this to be a reasonable belief.
You said that no woman has ever been abused by a transwoman in a toilet. That's irrelevant. Women have been assaulted by men in unisex toilets, as well as victims of other sexual crimes such as voyeurism. If all our public toilets become unisex then it increases the risk of those sorts of crimes against women.