Does that sound familiar that when you see an attractive girl to assume that she cannot be single and therefore never ever approach her?

No. Attraction is not linear.

Every attractive woman is equally insecure from inside. She always has too much internal pressure to look her best all the time.
Attractive females are more single than you can think off.
1. Many people assume that they are taken or arrogant.
2. Many guys are just in awe with their looks. Thus more potential options in practice results in less actual opportunities.
3. People often respond to their outer persona and hence more often than not interactions with them are superficial.
Many attractive women do take pride is their looks but hate men who like them only for looks. It’s same feeling a rich man gets from a gold digger. They hate skin diggers. They love the attention but hate the premise.
Attractive women don’t like men who are ‘in awe’ with their short-lived beauty. They want to be treated naturally and normally.
Most good looking girls are in fact low maintenance. I know only one thing women truly crave. Masculinity, confidence and true love.
Don’t approach any attractive woman or any woman for that matter only for relationship. Start with friendship. Then see where it can go or not. Don’t pre approve them. You are also a selector. Women love this. They often make great friends but bad friendzones. Be natural. Be her friend. Save yourself for that special person. You will ultimately get that. More selective you become, better options you are bestowed with.