That's a complete mischaracterization of what your ideological opponents believe.
What we believe is that we have a better country when we have programs that provide for those who fall through the cracks and better when there is a social safety net. Since that must be paid somehow, the people best to be taxed are the wealthy.
Americans have been hearing your standard 'govt help breeds dependency' trope for over 100 years. Your 'theory' is that not helping people forces them to be self-reliant and more dependent.
Pre-New Deal, America had no social safety net nor programs that helped the poor or working laborers. Were there any fewer desperate poor people or fewer workers that lived hand-to-mouth? No. They weren't forced to be more self-reliant -- they just stayed dependent upon their means of existence.
Then, workers decided to organize to demand better pay and working conditions. It was first looked upon as un-American -- that only the bosses should set wages. The politicians in the pockets of the bosses sent the police out to stop organizing. So the workers, realizing they could vote, through out the anti-labor politicians. Labor finally was able to bargain with management and workers got higher pay.
Years later, seeing that senior citizens who worked all their lives, were destitute in the streets, created Social Security. Johnson, seeing that seniors and the poor couldn't buy health insurance, created Medicare and Medicaid, respectively. Johnson recognizing that black people were being discriminated against, wrote the Civil Rights Act and the constitutional amendment to ban poll taxes.
As we see from history, government programs that help people don't come out of the blue -- they are a reaction and response to social and market failures.