We're already giving money to people with no job, this would effectively take money off people who administer welfare systems and give it to low paid workers who would then get benefits and wages.
Not at all. It gives money to everyone regardless of income. Welfare makes up a small percentage of GDP (unless you include all entitlement programs which this wouldn't). A basic income would be a huge percentage of GDP. IIRC in Switzerland's case this is about 25% of GDP. That's a massive increase in government spending.
You missed my (admittedly subtle) point. Yes, on the face of it, it gives a basic income to everyone. But you haven't magically made more wealth so your average tax payer has to pay somehow. Either through higher taxes, a devalued currency, or fewer schools/hospitals. The people who do stand to benefit are those who would have been earning just enough to stop receiving welfare before. They now get to keep the benefits and the transition up the income scale is smoother. Meanwhile, those people who had a job administering welfare are out of work.