I see it for a specialized solution for a specific class of problems, which can lead to surprises if your problem evolves. There are always trade-offs to be made (performance, flexibility, hardware cost, etc.), asyncio just has different characteristics than the alternatives. Maybe since a upper bound of concurrent users it is always a great (the best?) solution, someone with more experience along all the design and requirements space could comment.
I find it interesting when someone mentions that X is bad for something it was not designed for, as much as I am interested when someone mentions that X is good even if it was not designed for something.
You can't mix non async code with async. And you can easily do in some way and block your application without you noticing.
And in the end, async is not even really async, just cooperative execution.
I'm a big fan of Python since very low version. And I don't have too much difficulty using async/asyncio now I'm used to it, but in all honesty I don't think that it is really great in the grand scheme of things.