Secondly, you can't actually redistribute GDP. You could (in theory) take 100% of the profits of all businesses, that would add up to about 12% of GDP:
https://static.seekingalpha.com/uploads/2018/8/30/saupload_B...
Notice the drop around 2008? That's what happens when a lot of debt can't be serviced anymore.
Lastly, "society as a whole" doesn't contribute to anyone's success. Just because you are a member of society doesn't automatically imply you have done anything for anyone. If I was offered a UBI on an Amazon's worker's salary, I would just retire, or at least drastically reduce my workload. A lot of my money goes towards my retirement anyway, so why bother?
This is entirely different from a "subsistence UBI", which I do support in principle.
For the rest of your tax money, there are concrete places that those are going to and if you don't like them, we can altogether as a society do something about it. And guess what, with UBI people will have a lot more time and freedom to spend on actually participating in politics.
Sure, in the end it might bumps it up from 1/3 to 1/2 maybe, but you are getting a lot of that back anyway as UBI to yourself. Even at 1/2 I don't think its unfair.