The plan is to update the Ethernet library to support both shields as well as the W5200.
A pull request for this was submitted in 2014 (#2325), before the Ethernet Shield 2 was produced:
It was not merged, possibly because it was not required to support official Arduino products, but it was not rejected either.
Once .cc and .org resolved their conflict and .cc started selling the Ethernet Shield 2, it became more important to offer better support for the W5500 Ethernet controller chip used on that shield. During some discussion of this:
Paul Stoffregen announced that he had already created an improved Ethernet library that supported all 3 Wiznet chips. The discussion then moved to the Arduino Developers mailing list:
After a bit of back and forth there, Cristian Maglie stated that he was going to go ahead with merging #2325 but Paul Stoffregen requested that he instead wait for him to complete work on his Ethernet library. At last report, the Paul Stoffregen library was still not ready to replace the stock Ethernet library. It was suggested to go ahead with #2325 after all but momentum seems to have bogged down.
We are seeing much less reports now of people trying to use the Ethernet library with the Ethernet Shield 2, which was a very common problem after its release, so I guess the word has gotten out about using the Ethernet2 library. This has made for less motivation for the Arduino developers to make this happen. I'd really like to see things get moving again. I use both W5100 and W5500 so it's much more convenient for me to use a library that supports both. I was maintaining a fork of the Ethernet library with #2325 merged for a while, which some people found useful, but since it seemed that an official replacement was soon to come I stopped maintaining it and it is now a bit outdated.