I agree it would have to be based on what people need, although this is of course debatable. The level of JSA is ridiculous and I defy anybody to live on it for long. I expect most people could survive for a couple of months, but not when the washing machine or boiler breaks or there's a fault in the wiring, which means there's no electricity or when a child needs a new pair of school shoes, etc.
Higher earners, who might have to pay the most, would also receive the money, which they would be able to save, so might even be better off too.
The current way of working out MIS, however, undermines the idea of a CI, because it looks at household income, whereas a CI would pay all individuals the same (maybe on an age-related sliding scale).
The big thing, as you've already written, is that millions possibly billions would be saved on the administration of means-testing and work programmes.
Something needs to happen, because the future is short-term contracts and zero contract hours and nobody needs a crystal ball to see that. A civilised society needs to accept that every citizen should have a minimum income. If somebody can then earn an extra £50 from doing a little job, they should be able to keep it rather than having it deducted from JSA, which is what happens at the moment. And woe betide anybody who is offered a week's work, because the claimant then has to come off JSA and start all over again - and ends up worse off anyway. Universal Credit is even worse in this respect.