Nope, there is no problem, that simple, and done. The audiophile is always looking out for problems in order to *not* enjoy the music. Sounds weired, but so it is. Just so.... a complex set of compromises that don't lend themselves to simple yes or no answers.
No, there is no difference analog versus digital, and IIR can be as good as it gets.... excess group delay. This is cumulative and builds up from every crossover in the system. Like the example kimmosto showed above the lowest and steepest crossovers (IIR/analogue) cause the most harm.
Subjective, sighted preference is not a predicator for anything. Most probably it is pure imagination--we had that so many times with so many mysteries. It was never proven that people in an ordinary situation could detect or even 'prefer' a certain group delay or just none.There is then the impact of the room, whether the speaker has a perfect step response or dreadful step response it will still be affected by room interaction. ... Rooms introduce non minimum phase artefacts and the cumulative effect of these can create an extra layer of excess group delay. While it isn't advisable to try and equalise most of this you can with careful processing bring the response at the listening position back towards minimum phase. I find that overall this has a positive impact on sound quality but is source dependant and can sometimes make things sound less energetic.
And reiterated the common saying from the 'golden ears': "picking the difference would be hard for most". Should I now feel a deficit with my hearing? Me suffering because I can't enjoy the delicacy of my stereo, or can't fairly worship the stereo of somebody else? To the contrary, I'm happy to just dismiss the idea of that violent imperfection in 'time response'. I'm glad with the the music given to me.Making a speaker time coherent above 600Hz is going to be subtle in most cases (of reasonably well engineered speakers to begin with). With casual listening and studio recordings picking the difference would be hard for most. But with time and naturally recorded source material of real instruments in real spaces some difference can be heard tending towards making things sound more realistic and true to life.
Real instruments in a stereo recording? I know a few musicians who are in the recording business. They actually do not like the sound of recorded instruments to put it mildly. A recording is something else in its own right, not a replica of the real sound. To talk about "the real" is a typical, if not the original audiophile's fairy tale; only the naive, not familiar with the real thing can believe it.
Below 400Hz the difference is much more obvious and can be a combination of effects from the speaker itself and the room.
Rod Elliot has quite a good article that describes the mechanics of some of these things
You actually must not equalize the room's group delay in bass and lower mids. The hearing needs it!
The latter link is well chosen. But to make the point even more clear, read that chapter first: https://sound-au.com/ptd.htm#s4 You may feel that it isn't necessary to dig further. Dr Toole is a highly respected scientist with speakers being his dedicated working field. One cannot have an opinion on science. If you distrust it, prove it!