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If anything should be changed, I would say the docs.  Though
I disagree with the send during a call to push(), for most
users, it makes sense, and convincing the current maintainer
that removing the send on push for the sake of async purity
would be difficulty (practicality beats purity).

I believe that adding a note which reads something like the
following would be sufficient.
"The default push() implementation calls the underlying
socket send() (to increase data throughput in many
situations), and upon error, will call handle_error().  This
may cause unexpected behavior if push() is used within a
subclassed handle_connect()."