Well, eBay allows people to sell things to each other across the world/country which solves a different problem. Most of the people selling things on classifieds have no interest in having to go to the post office to ship your item and deal with paypal or something to get money. The items on these yardsale groups sell within minutes and someone comes to your door with cash in hand and the item is gone. People really like and trust the community aspect of selling things this way.

Plenty of people buy and sell on ebay within small local communities with a pickup only option. The trust factor comes from being in the same community and doing at least one good transaction. The mode of payment has nothing to do with it. In fact, it would be better if you didn't have to deal with cash.

Just because things have been done in a certain way doesn't mean they can't be done better.