...Of course, I would still rate those as the strongest arguments as far as what the purpose of taxes should be. Anything not for group-use (and this includes handing out charity) can be done by individual people and/or organizations
Yeah, we are on the same page.
I believe these group-use services have to be paid by compulsory taxes, because these services cannot exclude any particular non-tax-paying person from consuming the service.
Wealth redistribution is a function of taxes in current societies, but not a primary purpose of taxes. Wealth redistribution is more of a moral obligation and/or political tool.