Echoing others here. It's all about connecting with a potential date.
When I interact with a man, no matter how short, we are connecting. Provided it's pleasant I'll be happy to receive his number or give him mine when asked.
Giving my digits to some random man I've never even spoken to or, worse yet, seen in my life is highly unlikely. I'd have to be incredibly attracted to him somehow for it to work.
Remember that a 'direct' approach whilst efficient ignores one key detail: we choose whom to give our time and attention to based on how they make us feel.