There is no one size fits all answer. If my mother 'put her foot down', but didn't bother to have a good reason for it, I quite blithely ignored her. I turned out just fine, especially compared to my sisters, both of whom played her game.
Rules and structure are wonderful things, but to actually work, they must be both A) reasonable, and B) consistent. If they fail on either of those accounts, well, kids are smart, ultimately, they will do their own thing anyway. Try too hard to make them who you want them to be instead of who they are, and you may just end up with a relationship like the one I have with my aunt, where I moved 2000 miles to get away from her, block her emails, stamp all mail 'return to sender', block her phone number, and threaten to call the cops if she sets foot on my property or comes within fifty feet of my kid.
So, is a sixteen year old responsible enough to date?
I have nine cousins between the age of 15 and the age of 17. Starting from youngest to oldest, the answer to your question is:
yes, no, no, yes, yes, yes, no, yes, no.
If you want it separated by gender, than youngest to oldest for the boys is:
no, yes, yes, no
And for the girls:
yes, no, yes, yes, no.
I know a sixteen year old that I would trust with more responsibility than I do her forty year old mother. I also know a five year old I would trust with more responsibility than another sixteen year old of my acquaintance.
I hope that clarifies the issue for you.