You mean it discourages marriage, not welfare, correct? If so, you are so right (and this has been known for 50 years). At first the father would still live there (without the government’s knowledge) and still function as a father; now they’re way past that.
Yes, welfare discourages marriage.
And since a married couple invests and saves more than unmarried couples that make the same income, as well as invest more effort into the children, the breakdown of marriage is why a couple trillion dollars has done nothing to affect poverty numbers.