It would have to be third and fourth spaces though. Would it be right for transmen and transwomen to share spaces?
The discussions I've seen have always been to create single, whole floor to ceiling room cubicles, with sinks inside them, like disabled toilets but without the need to make them wheelchair accessible. So safe, private, dignified, regardless of TW, TM, M, F, NB or frostgendered.
The real alternative is that women shut up and put up, and wait to be told on where the government put the line (this year, Stonewall will then work HARD on moving it) on which males use women's spaces. No, not going along with that one. There are real issues of safety, privacy and dignity, they have to be met, but women just getting used to absorbing anyone who feels like it with any motives into their spaces fixes nothing, it just makes the problem affect 52% of the population instead of less than 1%.
Cost - I suspect the government will be desperate to throw money at any solution now they realise what a mess they've made and how the consultation is going. And women are pretty powerful at fundraising.
No, third spaces aren't wanted. What is wanted for women to just shut up and get their clothes off, and stop acting like they should have a say in it.