binomial(link="inverse")

This isn't accurate. You are talking about link functions *known by name*.

     link: a specification for the model link function.  This can be a
           name/expression, a literal character string, a length-one
           character vector or an object of class '"link-glm"' (provided
           it is not specified via one of the standard names given
           next).

Nothing is stopping you giving the link as an object, and there is an 
example on the help page.  We made this easily user-extensible quite a 
while back.

As to why the list of links known by name is as it is, that seems history. 
in part the White Book history of S.  I've always thought it an error that 
'log' was a standard link for binomial, as the range does not match the 
specification of probabilities (and S did not do so, MASS Table 7.1 ). 
For each of log and inverse you have a valid model only for some values of 
the data, and can easily ask for predictions that give an out-of-range 
error.

 this may be a better question for r-devel, but ...

 Is there a particular reason (and if so, what is it) that
the inverse link is not in the list of allowable link functions
for the binomial family?  I initially thought this might
have something to do with the properties of canonical
vs non-canonical link functions, but since other link functions
(probit, cloglog, cauchit, log) are allowed, I can't think
of any good reason.  In fact, it's sort of a mystery to me
why the sets of link functions for each family are restricted.
Is this from painful experience that some link functions just
don't work well?

 I can go ahead and hack my own version that allows inverse
link, but it would be nice to know if I'm doing something dumb.

 (The reason I want to do this is that the inverse link
linearizes the Michaelis-Menten function, y = a*x/(b+x) ...)

 cheers
   Ben Bolker

Brian D. Ripley,                  ripley at stats.ox.ac.uk
Professor of Applied Statistics,  http://www.stats.ox.ac.uk/~ripley/
University of Oxford,             Tel:  +44 1865 272861 (self)
1 South Parks Road,                     +44 1865 272866 (PA)
Oxford OX1 3TG, UK                Fax:  +44 1865 272595