Improving an individual's happiness means nothing in the face of the economy.
Let's assume this: you give welfare benefits to the unemployed that ensures a standard of living pretty close to minimum wage. Now, assume that A is a minimum wage worker. A is now less willing to accept his minimum wage check because he can get more benefits by simply stalling at home and doing nothing. This creates incentive to not work, which, in turn, greatly reduces the efficiency of the economy.
That much welfare is an extreme example; however, even if a government has surpluses, giving things to less fortunate people on a large scale has its impact on the economy. Let's assume that A is starving and can barely eat two meals a day, neglecting the influence of social factors; that individual is now more willing to do whatever he can to get his son or daughter a proper education and ensuring that they will not suffer the same fate. Assume that A is making a decent living; he might suddenly want his daughter and son to have a PS3 in their homes, but overall, he has less of an incentive to do this. It's the exact same reason why grains collected from agricultural support isn't just given to poor countries despite our ability to easily do so.
Not deserving it is a rather funny argument, though; people who work at construction jobs are arguably more important to societal infastructure than, say, a programmer for a game design company. Why does he not deserve welfare when healthcare and retirement benefits are readily provided to the more "deserving" programmer?