Like the other poster said, context is key. Strike up a conversation with a person you don't know, enjoy it, and want to talk to them more? Ask away. And bars and things might be appropriate so long as you quit if they say no.

The main thing with the "random person you've never spoken to" is this: It might be something you do from time to time. It might be something she deals with once or twice a week - or daily. You might be respectful and asking, but many others aren't. If you haven't even had a brief conversation, she likely knows it is all based on looks and absolutely nothing about her personality.

You won't personally be harassing her, no. But overlooking this stuff is being ignorant of how she might be treated on a daily basis and it can make you part of the problem, depending on the context of the situation. It isn't like it is hard to simply move on: You likely do this with people that aren't prospective dates in your eyes.

Context is key. In a bar, it might be OK. (This is not a blank cheque I'm giving you, you still need to think about a lot of things!) In the métro, I'd say yes, in almost all cases it would be unwanted. Unwanted forced interactions with strangers are harassment.

Yes, it's sad that you may lose the love of your life this way. It's sadder that many women lose their actual lives over this kind of thing.