I see your point and agree with it, but the difference is in the ease of delivery. Unsafe public transport has obvious solutions - increase police numbers, increase surveillance, train police and security staff in what constitutes unacceptable behaviour, actually ban or fine those who engage in such behaviour. Unfortunately those solutions would be extremely costly and come with their own raft of issues.
Firstly the police don't exist in a vacuum, many of the attitudes which lead men to assault or harass women are also prevalent in the police, which is why report rate for such crimes are so low and why so few reports actually get acted on. In order to be effective, police on public transport would need to be deployed in numbers high enough to be able to deal with groups of rowdy men and have the will to nip intimidating behaviour in the bud which some would dismiss as 'harmless banter'. And even then you aren't protecting women who are wary of the presence of men full stop because of previous experience.
And then you have another problem which is that when you've identified troublemakers, transport providers actually have to have the will to punish them. Unfortunately because of certain attitudes in society, the very same people who will use the train without incident to get to work can, with a few drinks in them, commit an act of harassment or assault which would warrant a ban. I'd personally have no problem fining or banning depending on the severity of the crime and let them deal with it, but I doubt transport providers will be so willing to risk losing a decent proportion of their custom.
This is all to say that, clearly women-only carriages don't solve the underlying problems of misogyny or the wider problem of crime on public transport, but it's a cheap and easy way to protect a section of vulnerable people until we can actually get our act together as a society. Unlike most people who are victims of crime on a night-out, women are targeted by men simply because they're women, so making them feel safe is often simply providing an area where there's no-one to target them. Tackling other forms of crime is no less important, but because the factors involved with violence between under-30s men are far more diverse there's no such 'easy fix' that will protect people in the short-term.