Reducing administrative overhead specifically is pointless. It's looking at one part of the cost while ignoring everything else.
The relevant question is costs - benefits.
The cost of Basic Income is $20k x # of adults + overhead. The cost of Basic Jobs is $20k x # of adults willing to work who can't find work + overhead - value of labor provided.
I'll make up some USA-centric numbers to illustrate the calculation.
Suppose overhead for BI is $50/year and overhead for BJ is $5000/year. Suppose further that there are 250M adults, 50M of which are willing to work but can't find work. (The remaining 200M will keep their current job.)
Cost of BI is $5 trillion, cost of BJ is $1.25 trillion. This assumes that the Basic Jobs provide no value whatsoever and Basic Income provides no disincentive to labor whatsoever.
If you disagree, please cook up your own numbers and show me how this could be wrong. I'm just curious to see any mathematical model where BI makes sense - I haven't been able to come up with one myself.
It doesn't acheive the goal of reducing administrative overhead, since actually creating jobs has considerable administrative overhead.
It also doesn't achieve the goal of increasing labor mobility and facilitating experimental, entrepreneurial endeavours.
In fact, it doesn't do much of what Basic Income does.