I agree that something like a negative income tax would be cheaper with fewer downsides. But it would be spun as "subsidizing Walmart". You see that today when politicians criticize part time Walmart employees for still being eligible for benefits.
Imagine if some low wage employer could pay you $10 an hours and government throws in an extra $5. If the market clearing rate is $15 for an employee, giving a subsidy of $5 pushes the wage down to $10 (effectively $10). They could offer $15 (effectively $20), but then you have a misalignment of quantity supplied and quantity demand, which would result in too many applicants and having to select on non-economic terms (e.g. overpaid do-nothing internship going to the CEO's nephew)
Imagine if some low wage employer could pay you $10 an hours and government throws in an extra $5. If the market clearing rate is $15 for an employee, giving a subsidy of $5 pushes the wage down to $10 (effectively $10). They could offer $15 (effectively $20), but then you have a misalignment of quantity supplied and quantity demand, which would result in too many applicants and having to select on non-economic terms (e.g. overpaid do-nothing internship going to the CEO's nephew)