An unmotivated, largely unsupervised park fence painter might not achieve much in the way of output for their $7.25 per hour, but importantly they aren't being paid $7.25 per hour to enjoy their chosen form of leisure. Which means that when someone in the private sector wants to pay them $8.50 per hour to work hard creating $10 per hour worth of value, they might actually consider saying yes. Any value the "basic jobs" themselves add to society is just a bonus.
I don't see why the administration of "Basic Jobs" would be any more open to corruption than any other bureaucratic role, many of which administer things far more significant than next week's work assignment to people earning far more than $7.25 per hour. It doesn't seem unsurpassably difficult to design a set of rules to ensure that "basic jobs" are rotated and not too cushy or unpleasant; I'd actually see that as an easier task than calculating a level of "basic income" that doesn't grotesquely distort one or more of (i)low-end labour supply (ii)budget balance (iii)price inflation and (iv)rental yields on substandard property
There are two kinds of people: those who escape work or are incapable for it, and those who work fairly (but may still be poor).
Former are going to build a lot of bad fences, for $7.25, but business only want latter ones. And if you have Basic Jobs, they would indeed be working for $8.50 in poverty, but if you have Basic Income, those would be working for an equivalent of $7.25 from BI and everything their fence-needing employer can conjure on top of that, which will hopefully give them something around $15/hour, which might let them get out of poverty actually.
Low-end labour supply is poor people. Low-end labour supply is people you pay not enough money for them to escape poverty.
Any effective fight with poverty would involve disrupting the "low-end labour supply" as we know it today.
I don't see why the administration of "Basic Jobs" would be any more open to corruption than any other bureaucratic role, many of which administer things far more significant than next week's work assignment to people earning far more than $7.25 per hour. It doesn't seem unsurpassably difficult to design a set of rules to ensure that "basic jobs" are rotated and not too cushy or unpleasant; I'd actually see that as an easier task than calculating a level of "basic income" that doesn't grotesquely distort one or more of (i)low-end labour supply (ii)budget balance (iii)price inflation and (iv)rental yields on substandard property