I think 'because they are male' is a perfectly satisfactory reason for excluding transwomen from spaces designated for women.
The UK Supreme Court has clarified that in this context the word 'woman' means 'biological woman'.
That in itself should be all that biological males, however they identify, need to know, in order for them to respect the law and stay out of spaces designated for women.
I don't see any 'societal cost' to this excluding men however they identify from women's toilets - society has operated on the basis of separate toilet facilities for men and women for a very long time, and it has been respected by men for a very long time, so continuing that configuration is more embedded in society than the very recent, highly contested claim that a subset of men have the right to use women's single-sex facilities.
Statistical data about the risk of transwomen causing harm to women in women-only spaces is an interesting and very serious topic, but it's not the only reason why men, however they identify, are excluded from women's spaces.
More immediate reasons are 'It's the law' and, in the workplace 'It's company policy and if you continue to breach company policy it is a disciplinary matter'.
'Respecting women' would be a nice reason for men to stay out of women's spaces, but that seems to be too much to ask.