I suggest changing the “except” clause to “except BaseException”, which would make the intention clearer.

As an alternative, see also my Issue 23430, were I proposed not catching exceptions like KeyboardInterrupt and SystemExit, by changing this to:

try:
    self.finish_request(request, client_address)
except Exception:
    self.handle_error(request, client_address)
finally:
    self.shutdown_request(request)