I thought the 'myth' was that stuffty people abuse the system too easily so that they can buy too many shoes and phones. Like for example: the large black woman who always pays for her 100 dollars worth of food with food stamps and then buys 1200 dollars worth of wine with her own money every week.
I literally only hear these kinds of anecdotes from people who have basically zero interaction with anyone on food stamps/welfare/etc.
There's definitely flaws with how welfare programs work, and sometimes the programs incentivize staying on welfare rather than pursuing a higher paying job and losing your benefits. But I don't think the solution is to kill off the entire program just because someone's got some sort of hearsay story about a 'welfare queen' using food stamps for lobster.