You're saying that welfare produces downward pressure on wages. But I believe it's the opposite: If someone paid you $1,000,000/year whether you were working or not, if you're rational you'd never take a job that paid less than the marginal value of your leisure time. The latter is substantially improved by having $1,000,000/year of unconditional income, of course!

Welfare dollars (at least the unconditional sort, unlike, say, EITC, which is deliberately a wage subsidy) are in competition with employers for their potential employees' time and effort, not a subsidy.