Here is my two bits about this, I know some of it has already been said, but here goes: I think the problem of muddy bass is not a flats vs rounds thing-that's a correlation, but not a causation. As far as I can tell, a bigger issue is the trend of how bass sound is approached in general. The overall movement has been towards what I would call a hyped low end- excessive amounts of 50-150hz. I could go into what I think are all the driving factors for this, but that is another topic that has been covered extensively in other posts. Suffice to say this movement towards a hyped low end has permeated every corner of the bass world. The porting of modern bass cabs is almost always tuned to these frequencies, and many modern bass amps seem to be voiced to bring out more of these frequencies. Add to that that most of said amps also now have DIs built in, which means that bass is more often than not run through the FOH system, and said FOH systems more often than not are excessively large for the room, and include subwoofers. All that combined is a perfect storm for mud. I don't think that flatwounds are inherently muddy-James Jamerson's playing never sounds muddy to me, nor does Carol Kay's.
The bigger problem as far as sounds being muddy is the "wash of bass" approach to sound, plus a lack of realization on a lot of bass players parts that what often the frequencies that make and amp/cab combination sound "fat" when played by itself and at moderate volumes (like when testing out rigs at a guitar store) tend to turn into mud in actual gigging situations, particularly when things get loud. The one role that I can see flatwounds vs roundwounds playing in this is that rounds will give you some additional high end to balance out the ridunculous amount of artificial lows that are pumped in by all these additional factors.
