When I buy from eBay, I like a BIN. I don't have to set up an auction "swooper" and I get the item right away.
A also use BINs when I sell on eBay. Usually on a big-ticket item with a reserve. The reserve will keep the BIN around even when there are bids on the item. Once the reserve is met, the BIN goes away. I probably sell about 30-50% of my stuff on a BIN. I set my price fairly, but a little higher than normal. Most people are willing to pay for instantanuous gratification.
BTW, I never sell an item before the end of the auction and I have never asked someone to sell me something early. I have asked someone to sell me something after the auction ended with no bids. Usually it's because I started looking for the item after the auction had already ended or I missed the auction, not because I didn't want to bid.