A large advantage to paying with cash is the seller, who probably needs the money in order to buy another house, knows that the sale will not fall through due to financing, etc, and that you can move quickly.
If for example someone makes an offer with 0% down, while they might be preapproved it's far more likely their mortgage application will take a while and/or not work than someone paying 100% down.
Consider that if you sell your house and make an offer on another home, but the sale of your home falls through because of mortgage issues. A non-insignificant percentage of mortgage applications get rejected and as a seller you probably can't know in advance who those will be. Higher percentages down likely decrease this likelihood, though, which makes higher % payments more attractive.