In the game of "who's paying," servers are the referees
The average human restaurant-goer spends hours of his life arguing with dates and friends over who pays the bill while waving credit cards at a server. This game can go on as long as the server allows, and ends when he grabs a card and walks. Now you're just left arguing over who pays the tip.
Giving the server your card at the beginning of the meal is an accidental source of stress
A surprising number of customers will bypass a discussion of who pays by slipping the server their credit card early in the meal. For the customer, that means nobody can fight him when the debate about who's paying starts. For the server, the result is a pocketful of added responsibility and added stress when it comes time to remember which card goes to which table.
Servers hate Groupons and gift cards
The main reason? The overwhelming majority of customers using Groupons see nothing wrong with tipping at a 50% discount, despite the fact that the server is still functioning at 100%. As for gift cards, well, a surprising number of people see them as a free meal, and count tip as part of the deal, leaving those busting their humps empty-handed.