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.
Yes, fans go supersonic at max power (takeoff and sometimes max climb, especially at lower altitudes). And yes, that causes the well known 'buzzsaw' noise. For takeoff and initial climb, max thrust trumps fuel efficiency.
However you'll notice the 'buzzsaw' noise goes away at cruise, when fuel efficiency is the primary concern. At cruise power settings the fan tips may go supersonic, but just barely - nowhere near 1.5 Mach. Creating shock waves is simply not efficient (unless you start talking about something like a Ramjet/Scramjet, which use an entirely different cycle relative to fanjets). If you look at the newer (relatively) high speed turboprops, you see highly swept props at the tip - for the same reason you see swept wings on jet aircraft. It delays the onset of supersonic flow...
BTW, 1.5-1.6 max pressure rise is pretty typical for the fan portion of fanjets at high power.