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BaseHTTPRequestHandler in http.server supports HTTP/0.9. But the response for HTTP/0.9 request is implemented wrong. 
Response of HTTP/0.9 request returns message body directly without status line and headers. But if you inherit BaseHTTPRequestHandler and set the default_request_version to "HTTP/1.x", then self.request_version can never be "HTTP/0.9" since in the https://hg.python.org/cpython/file/tip/Lib/http/server.py#l315 branch it does not set version to "HTTP/0.9" and then always sends the status line and headers back.
A trivial patch can fix this problem that set version to "HTTP/0.9" in the branch. But this will cause some failure in tests. The tests in test_httpservers use http.client.HTTPConnection to send and receive HTTP message. But since 3.4, HTTPConnection doesn't support HTTP/0.9-style simple responses. We can use it to test HTTP/0.9 connection if the server is implemented in the right way.
And since http.client.HTTPConnection has dropped the support for HTTP/0.9, is it reasonable to drop the support in http.server too?

can should be can not.
And not only HTTPConnection, support for HTTP/0.9 seems to have been totally abandoned since Python3.4 in http.client.

As I understand it, you are saying if you override the undocumented (but publicly-named) default_request_version attribute, HTTP 0.9 requests no longer work.
I suspect it is even broken by default. My understanding is with HTTP 0.9 you should be able to send b"GET <path>\r\n" and get a response, but Python’s server will deadlock waiting for a second blank line or EOF. It looks like this deadlock has been there since ~forever (1995).
See Issue 10721 which already proposes to remove 0.9 server support. I would be weakly in favour of this (or more strongly if someone can prove my theory that the current support is broken).

I think you are right. Simply run http.server.test() and then telnet to send "GET /", the client hangs. Or add a timeout to BaseHTTPRequestHandler, you can see the timeout error on server output.

Since my last comment, I have become more confident that Python’s request parsing never supported proper HTTP 0.9. So I would prefer to remove it in the next version of Python, and not bother fixing Xiang’s bug in existing versions (unless someone offers a practical reason to fix it).
For the record, this patch is what a fix might look like.

> So I would prefer to remove it in the next version of Python, and not bother fixing Xiang’s bug in existing versions.
+1. In rfc7230, "The expectation to support HTTP/0.9 requests has been removed".