It is documented as deprecated, but only in the 'seealso' note at the top.  I think it would be reasonable to open an issue to add an actual 'deprecated' ReST tag to the docs.

For your 1 and 2, the stdlib smtpd forwarding is also blocking; that code appears to be copied verbatim from stdlib smtpd.  It needs to be replaced with calls to aiosmtplib.  Feel free to submit a PR :)

For your 3, that design is so that you can run the smtpd server as part of a non-asyncio application (eg: for testing, which has always been the main purpose of this module).  For an asyncio-only application you would not use a Controller (unless you wanted to offload the smtp traffic to a different thread, of course, then it would be useful :)