How long before this happens in the US?
I feel like we wouldn't let this happen as easily, there would be a public outrage. But then again, we let NSA happen. So maybe not.
I don't think this could happen in the US. The FDIC insures all bank deposits up to $250,000 per depositor per institution. The bank would have to fail first and after that it could only apply to deposits above the above limits.
Banks already pay the FDIC an insurance premium based on how much money is on deposit at their bank.
I doubt that would make any difference. As you pointed out, FDIC insurance pays out when banks fail. I doubt it covers government theft.

Besides, even if FDIC insurance would somehow cover it right now, I'm sure they'd find a loophole or change the laws so it won't.
In the US they'd just print 0.03% more dollars. Lot less likely to cause public uproar.
Not that I want the government to do that, but I'd greatly prefer that to messing with bank deposits.