This throws an exception and crashes your DocXMLRPCServer when using registered python functions that use function annotations.

Seems inconsistent to me.
Or is there a reason for this?

"This" refers to the summary of the bug.

Can you provide a test case which reproduces your issue?

Okey ...

Consider you have a function:
def fn( str:str ): pass

That you register to your DocXMLRPCServer:
register_function of SimpleXMLRPCDispatcher stores the function object  in the dictionary self.funcs under the name of the function (as key).

Then you start your server and access (with a browser) the ip and port of the machine running your xmlrpc server which calls
> DocXMLRPCRequestHandler.do_GET which
> generate_html_documenation() which copies the funcs dictionary into methods and hands it to
> ServerHTMLDoc.docserver which calls for each function name + function object:
> ServerHTMLDoc.docroutine which calls (for inspect.ismethod and inspect.isfunction):

inspect.getargspec on the function object

which will fail if you register an annotated function (like the above "fn") in the first place:
=========================================
  File "/usr/lib/python3.1/inspect.py", line 789, in getargspec
    raise ValueError("Function has keyword-only arguments or annotations"
ValueError: Function has keyword-only arguments or annotations, use getfullargspec() API which can support them
=========================================

Which most probably leads to the conclusion that you should just use the getfullargspec instead of getargspec just to avoid that the XMLRPC server crashes if someone registers a annotated function.

If you want an example:

pydoc3.1 xmlrpc.server

2nd usage pattern

change "SimpleXMLRPCServer" to "DocXMLRPCServer"
change function signature from "pow(self, x, y)" to "pow(self, x:int, y:int)"

and your good to go and have your doc xmlrpc server crashed the moment you send a get request to him (e.g. by accessing "http://ip:port" in the browser of your choice).

If you want I can send you a patch.

A patch with tests would be an excellent thing to have.