The thing is, charities and churches are rarely "run well". Many charities have become a cash cow for their executives and office staff (“Hey, look, we can direct a lot of these donations to paying us extremely generous salaries”), with actual generosity to those in need almost seeming an afterthought. I saw this firsthand when I volunteered in the central office of a charity, and it rather shattered my idealism.
Churches have been notorious for either stipulating that recipients act in a certain church-approved way to get aid, or giving charity in the hope that recipients will convert. Either way, it hardly strikes most people outside that religion as "generous".
It is worth pointing to the Nordic countries, where private charitable endeavours have largely faded away with the rise of the welfare state, and even the local churches are happy to let the state take care of the feeding, clothing and housing business because the state enjoys economy of scale far beyond any church’s ability. In spite of the dwindling of private charity, those countries have less wealth disparity than countries fond of charitable activity. Consequently, some feel that charity is a just an awkward substitute for a functional state, not a good thing in itself.