Like Twisted, there are many projects that continue to choose to use gevent, and consequently (for either of those libraries) Python 2. They solve real problems, as does the codebase we extracted SuPPort from, and we hope to help these projects rather than shun them.
Additionally, asyncio doesn't provide the same user API that gevent does: automagic task switching. Whether or not you like that API is a separate issue.
Finally, even if a person has no interest in using SuPPort, we hope that it might provide her insights into problems she'll likely encounter when using asyncio (or Tornado or Twisted or eventlet or any evented system.)
But indeed, I don't think it would be a good idea to wholeheartedly adopt their stack. gevent wasn't even a good idea on Python 2, and I suspect the large companies that use it have built up an armor of best practices and workarounds for its glitches, which you won't know about if you start using it.
In fact the earliness of SuPPort's release serves to illustrate that the primary goal: demonstrating many best practices for building servers and clients, in any language or stack. As far as gevent goes, well, that's mostly an ecosystem-dependent turn of fate that continues to serve us well. A data point gladly share, but not the core message per se. :)
No one expects 2.7 to go away, that doesn't mean contributors want to deal with Python 2 when 3 is available elsewhere.