I'd say it kind of depends on what your student is wanting to achieve with it - if they want to play classically (e.g. in orchestras etc) , or study music academically, or take grade exams (not sure where you are but here in the uk lots of people take grade exams as part of the learning process) then I guess they would need to learn the 'standard' classical ways of doing things simply because if they don't other people will tell them they're doing it wrong and discriminate against them because of it, even if they/you/I don't believe in that kind of thing.

...but, if they are wanting to learn simply for the joy of playing, then you might well want to be more flexible. I guess what is important is to take a look at the limitations of playing a particular way (whether that is the 'standard' way or not) and help your student be aware of these for themselves. For example, certain ways of holding the bow may reduce the flexibility in the wrist which might limit what you could do with it a bit further down the road, even if it doesn't seem to make any difference at whatever stage of development somebody is at.

I can only speak from my own experience but I learned classically and was taught to hold the bow at the frog, and now having not had a lesson for well over 10 years and having done a lot of folky playing in the interim, I now hold the bow about half way down at the point where it balances, which I like for the control it gives me from a rhythmic point of view. BUT I'm not sure I'd teach somebody to hold the bow there from the outset because it does limit what I can do in terms of long bow strokes... which I know I can do if I need to because I learned the other way first but if I'd learnt 'my' way all along I might not be able to switch.

I'd hope that anybody having lessons would eventually gain the confidence to develop a style of their own, with the support of their teacher. But to do that it would probably be helpful to know about all the different options, and to start at a point that doesn't limit anything too much.

sorry, that was really long and waffly wasn't it? :)