I agree, great insight.
Bolded - this is what I do, A LOT. I won't walk up to him necessarily but I will take advantage of an opportunity (like at an event or group setting) and begin chatting, and then wait for him to initiate exchanging phone numbers and/or asking me out.
It actually comes very naturally to me, when the situation is right.
It happened to me last week in fact, within one hour. Two different men. Just a natural and organic conversation that led to the exchange of numbers and a date being made with one. The other man I wasn't that interested in so took a pass.