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Changing it could break existing code written for the HTTP 1.0 behaviour. The main effect mentioned at <https://docs.python.org/dev/library/http.server.html#http.server.BaseHTTPRequestHandler.protocol_version> is that in HTTP 1.0 mode, a server may send a response without Content-Length, because its connection will be automatically shut down when it is done. In HTTP 1.1 mode, the server code has to manually set close_connection = True (or indicate the end of the response some other way).
Looking at the source code, changing protocol_version to "HTTP/1.1":
* Allows close_connection to be False by default (causing the problem above)
* Enables Expect: 100-continue handling (no problem)
* Changes the version actually used in the HTTP protocol (probably acceptable if everything else keeps working with a HTTP 1.1 client)
* Affects the SERVER_PROTOCOL variable for CGI scripts (unsure of the consequences)
Perhaps one way forward would be to use HTTP 1.1 by default, but still set close_connection = True. But then someone may come along and say Python should support persistent connections by default! It does not seem worth enabling HTTP 1.1 with non-persistent connections as the default.