No, they are... when they are. Often I feel there is the K1000 and then there is every other headphone. Staging, top-end and general live performance energy recreation can be so good. That said eliminating all the practical considerations of size, isolation, dedicated amp, portability, etc. and focusing solely on audiophile recordings, their low end is still problematic on a large minority of the well recorded music out there. And a lot of those tunes are wonderful and I don't want to compromise. I guess we all know this, but approaching solving that bottom issue brings in even more practical concerns.
Couple that with generally I dislike previewing every track in my head before deciding which phone to grab, I find myself often going back and forth between the K1000 being still underrated and overrated. Little comes remotely close in success, or as easy to demonstrate failure (across gear). IMO the 4070 performs better overall on that scale, though no doubt significantly behind the K1K on many [most audiophile?] recordings. From the comments of others, I optimistically hope JH13/3A+16 is in the ballpark (maybe even while used in a ballpark).