Wow , so now its wierd to interact with someone unless you know them ? What the hell aren't we all human beings jeez talk about social conditioning .
OP your doing yourself no favours by setting yourself these mental barriers , given the right conditions you will find alot of girls are quite happy some guy has taken an interest in them , looks/confidence/your social skills all play a part in how she recieves you though.
I've gotten girls numbers before , became friends / dated one , it's not impossible at all.
You will find most girls will find this wierd in theory but if someone they find attractive , confident and mysterious was to randomly spark up convo im sure they'd be wetting their pants.
Note - These PUA creeps with their 'daygame' and canned openers are bad examples
The context also plays a part e.g trying to talk to a woman in a surgery waiting room isn't likely to end well.
Social events whether it be gigs , festivals , bars whatever are your best options.