It does all boil down to having access to good information by which I don't mean anecdotal 'evidence' of how your auntie's neighbour's daughter's best friend got on with any particular method, but what the risks are in hard numbers (I like Trillian's list
) - and then you take your pick.
Of course all options should be discussed and offered.
And the risk of STDs discussed. And yy to lots of older people putting themselves and otheres at risk.
By which point IME a fair number of people's eyes glaze over because they 'just want the pill/jag/implant'.
You'd be amazed how many women I speak to do not want to know a lot
. They come with an idea of what method they'd like and reluctanctly take my leaflet with 'contraceptive choices'. Which I quite often then find in the car park bin outside...
Totally agree that this kind of in depth discussion, particularly about the feminist aspects of contraception, is not really at all common place in RL... Maybe it should be, but it ain't.
As far as all this talk about PIV or not, and the intrusiveness/riskyness of different methods go - well, we are free to make our choices.
I strongly believe that empowering women to want to seek this kind of information is what will make a difference.
'My boyfriend thinks I need to go on the pill' - WTF?? 

I am sorry, at the coal face of dealing with disempowered young people it is just of no use at all to say 'But what about non-PIV?'.
I do frequently point out that they do not have to have sex, but the pressure is immense - as somebody said about, that's a whole other thread!
And re having periods or suppressing them: well, prior to contraception a lot of women had a lot less periods because they were pregnant and/or BFing most of their fertile lives... not sure that would be preferable
.