Agreed BI would save on admin costs for benefits. But it's not going to solve the greater problem of economic rent extraction through land.
If we have more money they will take it off us via land. Saving on job centre costs makes us more efficient. Efficiency flows to the rentier. You'll be right back where you started with BI. Up BI and they'll up rent. And again.
In your example once you have your revitalisation and all the people pay taxes to build more roads and hospitals guess who's waiting for you with a big hat to shovel all the gains in? The land speculator. Up go the rents, up to the level where people have enough to live but no more. And back to square one.
Surely they deserve the gains, after all they are investing their hard won money? No! Fiat money takes no resources to create and the bankers will have your shirt. Private banks create money from nothing and "lend" it out if you promise to give them a cut of your labour as "interest" for 30 years.
Bank of England official blog:
http://bankunderground.co.uk/2015/06/30/banks-are-not-interm...