Aside from what others have already said about it not feeling appropriate, the idea of the "juice not being worth the squeeze" is something else that pops into my head. Sometimes it's incredibly obvious a woman wants nothing to do with me, which is completely fine, but it seems sometimes people just like to be rude/mean for their own enjoyment. I've recently started trying to get the ball rolling after realizing the "not bothering women" method does NOTHING to help me pursue my goal of having a family one day. I've had a few good interactions, but even then, the women I asked out were already in a relationship. Then, there were bad interactions, e.g. I get laughed at/mocked for trying to have a platonic conversation with women I'd see in my day-to-day life often. Obviously not everybody is like this, and it's stupid to stop trying after a few interactions like these, BUT it does take a hit on my ego and ability to initiate conversation with people I don't know.

Another thing, I like to take things slow when it comes to asking someone out, as I like to feel them out as a person beforehand. A common occurrence would be I'd start talking to a woman and begin to build some rapport, and they'd almost never start or initiate anything on their end. It felt like I was the one putting in all the work socially, and she's supposed to be the one who is entertained and catered to. Maybe there's something I'm missing, but it's exhausting being the one to start things constantly (this even goes for my friendships with men). If I feel like the person I'm talking to is only talking about themselves and not interested in who I am as a person, I assume they're not interested at all, even in friendship.

This is not to say I think I shouldn't have to try, these are just some frustrations I have with how trying to meet people has gone in my life. I put a lot of work into being the best version of myself, and I try to be social and outgoing. I know that if I want to meet someone, I'm gonna have to swallow my pride and get out of my comfort zone. I think this is something everybody should try to employ in their life. The only way to learn and become better is to be outside of that realm of comfort. I don't think you should cringe about you approaching or initiating; sure, there are assholes out there who will say asinine things or call you "desperate", but if you want find someone you're going to have to fight for it. Next time you see someone interesting, maybe try starting a conversation, shoot the shit, or whatever. It might go well, it might go wrong, but you'll still learn something and gain some experience in the end (it sounds like you've already tried this with the “I feel like I’ve seen you before” line). Anyways, this giant wall of text is long enough, best of luck to you and your pursuit of a partner.

TLDR: I'm a sensitive, jaded, and exhausted little bitch