Apparently the tips of large turbofans do go supersonic. The Trent reaches Mach 1.4 at the tips, supposedly. This allegedly causes the 'buzzsaw' noise.
There's a thread on the Tech Log some, 'Large Turbofan Noise' it's called.
Apart from the shrouding and close blade spacing, I myself can't see how the fan differs fundamentally from a propeller and those don't like going faster than Mach 1 (the Harvard had prop tips that could exceed mach 1 which gave it that slapping sound sometimes).
The fan air can't be compressed very much can it? Perhaps the close spacing of the fan blades allows the inevitable shock waves to be harnessed to good use???