I've got the HK system in my 2008 335i and I've always been pleasantly surprised about how good it sounded. I am an audio/video nut (I'm also an equipment reviewer for one of the larger U.S. based websites) and have some very good equipment at home. I've got a full set of Sonus faber Olympica speakers (IIIs for the fronts, Is for the surrounds, plus Olympica Center) in my media/theater room currently so you can judge my taste in sound off of those. I like accurate, but musical sound, speakers that can handle all genres of music equally well.
I have never felt the need to go aftermarket in my E90. Yes, I could drop a full set of Dynaudio speakers and some better amps into the car or add an additional larger subwoofer, but it really isn't necessary. With proper tweaking, you can get the Logic 7 system to sound very balanced and clear (without crossing over into the harsh or brittle sounding arena). It's funny because in 2008, the HK system was standard in a 335i. Now the HK is always optional in a 3 series (except for the M3/M4 perhaps) and just doesn't seem to sound as good. My 2013 X3 3.5 and 2016 X5 3.5 both had the HK upgrade and neither sound anywhere near as good as my E90's system. I firmly believe BMW has cheapened the drivers or amplification (or both) in recent years to pave the way for their more expensive B+O system which is frankly ridiculously priced - the system just isn't that good compared with what you could do aftermarket for the same money. Upgraded audio systems are a huge profit center for a car manufacturer in today's market so everyone is jumping on board.
My admittedly short listening to the QFs HK system (like 3 minutes and I only set everything to flat to hear what it sounded like naturally) left me with a "meh" feeling. It definitely needed to be tweaked but midrange and treble sounded ok, with the bass sounding a tad weak. Mid-bass punch was lacking too, but again, I did not fiddle with any of the EQ settings. A little bump in the 100-125Hz EQ settings could fix that or possibly a rise in the overall bass tone control could work too. I wasn't turned off to the overall sound, which was promising. I'm sure that with some time and EQ tweaking I could get it to sound at least decent. Deep Bass will most likely remain problematic, but midrange and treble should be fine. Mid-bass response could possibly be brought up to par with EQ, but without further testing I'm not positive on that.
If I buy A QF, I'll do some full range frequency sweeps on the system with some of my test gear to see what it is doing out of the box and how to best optimize the stock system.
Personal experience is that all speakers do improve with break-in time (some dramatically, some more subtle). My HK system in my E90 didn't change very much in the first few months of ownership. Neither did my HK systems in my X3 or X5. I'd imagine the HK in the QF will not change much either with time.