I'd say of course there is, but only to a point. Perfection or the perfect can, despite the name, is in the eye of the beholder. I guess, it's a misnomer by construct, but the fact that there really isn't a universal consensus as to what is perfect shows that what might be the ideal for one may not be the ideal for another. So yes you can improve on each headphone and others, but there will always be people who like or dislike one over another for whatever reason.
I look at it in a similar way that I think about balanced as is defined in the hobby. Back when the Lavry DA-10 came out, and yes I realize the Benchmark was already on the market already, people were talking about how mainly due to the fact that you could have a "cheap" balanced set up, that it would be "the wave of the future." There were discussions about increased slew rate, voltage swing, output impedance and others that balanced amps supposedly have over SE amps. Of course, over time some people realized or determined that certain SE set ups sounded just as good or better than some balanced set ups. Furthermore, here we are around 4 years later, balanced still hasn't gone mainstream despite the fact that there are even cheaper options out there.
So I think it's noble that somehow you're trying to find a more universal truth, but looking at my time in the hobby, there just isn't one, despite the fact that the data may be there to say otherwise.
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And to the above, which was posted while I was still writing my post, I agree. You can say you want to improve in certain areas and you may actually be able to do it, but there are limitations, as you've noted. And some you just can;t overcome. For example, I've owned the K1000 which are basically speakers that more or less have a headband, and while they might be somewhat speaker like, they do have their limits and IMO, while they offer certain things above the normal headphone, they also introduce certain problems as well; eg: they leak alot, IMO just as much if not more than a normal headphone, the fit can get really awkward and the seeming requirement that you need a power amp to sufficiently drive them.