
There is a part of the libertarian movement that advocates complete anarchy, that is not what most of us advocate.
Yes, social programs that coerce individuals to do good with other peoples money would go away. However, it is my strong belief, that through the creation of fair/just laws, most individuals in society will not have any reason to divide themselves along party, racial, gender, occupation, class, and other social lines. The unfair/unjust laws we create give power to discrimination, which in my opinion make it profitable for individuals to divide themselves. For instance who says a doctor is a more valuable member of society then a plumber? Well, for one you had to be told by someone and for them to make this outcome possible they had to legislate and advantage being a doctor over a plumber. (I’ll explain further at the bottom)

Freedom
Personally i think given the option of holding more of your money and having more say of where it goes would give individuals even more incentive to help their follow man. If their fellow man is truly in need.
The goal of a libertarian society would be to make sure all legislation pertaining to citizens is equal across the board. The extension of freedom would not destroy the ability to do good. You’ve been indoctrinated to think, the only way individuals will do good for others is through force and coercion, but there is no evidence to make this empirically true.
Our country is coerced into giving to Social Security, Medicare, Medicaid, Welfare, Unemployment to the tune of trillions of dollars. However, our society also willingly gives more than 300-400 billion dollars a year to charities. Could you imagine how much money could be given to charities each year without the threat of government coercion?
Do you know how many people would rather do good with their own money than use other citizens money to do good with?