I think as few services as possible should be single-sex.
The EA proceeds from the position that men should not be separated from women, in the provision of services. I think this is correct.
It (almost reluctantly) permits services to be offered separately to the two sexes (or only to one sex) under very very stringent conditions. This should be the very rarest of situations. It should only ever happen in a situation that admitting even a single person of the opposite sex would spoil the service or make it unworkable.
On that basis, service providers should have to pick: accept and engage in the sexism of a single-sex or sex-separated service, or work the service so that both men and women can be admitted. Letting in women and but only some, acceptable, men, is, frankly a cop-out. not to mention incoherent and unworkable.
services that could usefully be single-sex
That it would be "useful" isn't the threshold in law that a service has to meet to be offered to one sex only. As a test it understates and underplays the disdain we should have for single-sex services. We don't talk about services that could usefully be single race, or single colour.
My suggestion is to let the 'trans-inclusive' services exist if they must,
I say, no. If a service is such that it can lawfully be offered to one sex or to the sexes separately then it has already been decided by the provider that admitting anyone of the other sex is impossible. If it's possible that one man can use a service for women without spoiling it - then it must necessarily be possible for all men to do so. There is no deciding that some, nice, men can use this women's service, but not the other, nasty men. No men. Or all men.