Russ Roberts (of EconTalk fame) is fond of calling for less welfare and more private charity. His claim that private charity is more likely to get to the right people makes sense to me, but I think he underestimates the likelihood that voluntary contributions will be adequate to replace funds "confiscated" via taxes.*
According to this site, 2015 US federal spending on social security, unemployment, health, and labor costs ["charity for the vulnerable"] was $2.33 trillion, or over 60% of total spending. (These numbers do not include massive local and state spending on similar categories.) Meanwhile, total charitable giving was about $370 billion, or about 16% of the federal spend.
But what about the "effectiveness" of charitable giving? While some of it is self-serving, I agree that many smaller donors would mean fewer big mistakes, I also know that those donors would send money where it suited them rather than where it was "needed," as people are far more generous to "people like me" than the average, anonymous citizen.
Overall, I don't think charitable giving would rise by a factor of 6, if spending (and thus taxes) were cut back. The problem -- as usual -- is freeriding, which is much easier with voluntary contributions than it is with taxes.**
Bottom line: Every society needs a social safety net if it is going to call itself developed. In most countries those safety nets rely on complex bureaucracies and mandatory taxes to bring benefits to all citizens who qualify. In some cases, those programs can be improved (replacing means-testing with universal basic income or dividing security from savings [pdf]), but all systems will need to rely on taxes if they are going to deliver the quality of services the average citizen and voter expects.
* I tried to find the podcast where I made a comment on this matter, but my google-fu is weak.
** After Trump's corporate tax cut, "companies spent 37 times as much on stock buybacks than they did on bonuses and increased wages for workers." I paid 37 percent of my income in various taxes last year in the Netherlands, and I am happy to pay into a functional system :)