I don't think this is about independence, so I think that framing of the issue is wrong. I think it is about risk assessment, at both gut and cerebral level.
I think it's about being in a small, enclosed, locked space, with and controlled by one man, upon whose good will we are completely dependent, for an extended period of time.
And we've all heard of John Worboys and we've all met creepy men and men who just make us feel a bit uncomfortable and men we don't really want to chat to, whose innocent, friendly questions might make us feel a bit uncomfortable. Especially when we were teens, without adult confidence and social skills. We might not choose to lock ourselves in a car with such a man, or any strange man, if we can help it.
Especially for women and girls, avoidance is the most effective part of self-defence. We're usually going to lose a fight, we might or might not be able to run away, so avoiding placing ourselves in uncomfortable situations with strange men in the first place is a really sensible, as well as instinctive, thing to do.
Bus and train travel require independence but generally feel safe because there are a lot of 'harmless, ordinary' people around, whose presence is likely to deter some behaviour and who might intervene or witness other behaviour. You can move between train carriages, look for staff, call the police. With a bus or train you can get off at the next stop, if really uncomfortable.
So I think this is a case of risk assessment being very different for men and women. In terms of the risks identified and perhaps, how we identify them (or how we acknowledge that we identify them). Men can be risibly keen on saying they're discussing something 'logically', when they actually mean 'in terms of my own perceptions, prejudices and preferences' i.e. 'what I want here is...(I just think my thoughts are better and more important than everyone else's)'.
IME in life in general, gut feelings are usually an effective and reliable distillation of a lot of conscious and unconscious information. Whereas you can reason your way in or out of anything.
So if you were seeking to present 'rational assessment of the risks' as synonymous with taking account of cerebrally generated information only, or presenting this as a superior form of decision-making to taking reasonable account of 'gut feeling' too, then I'd say you were wrong and failing to acknowledge an important element of how risk assessment works. I say that as someone who values rationality and is blithely dismissive of a lot of 'woo' and all sorts of fears that people build up as stories with little foundation or experience.
In the end, you have to take risks or you'd never get anything done. If my plane falls out of the sky I die. If someone wants to rape and murder me while I'm out running, I die. My coba says both activities are worthwhile (risk is very bad but very unlikely). My coba for one session of an activity vs a likely slightly awkward, maybe uncomfortable ride home, might be different.
If you took the taxis together sometimes, knew the drivers and she could specify which driver she wanted, might that work?