The builtin function doesn't have the facility -- it is an m-file; you could make a local copy and modify the model inside that it uses -- on looking, it does use an explicit solution technique in building the model such that one could remove the constant ones() column.
I've not tried; so whether the following code is general-enough to not blow up if one does this blind fix I've no idea...
You might search on the File Exchange to see if anybody has provided alternate tools...
Does seem like reasonable enhancement request fodder; how likely it would be to percolate to the top of the list I'd guess might be pretty low in our lifetimes, though... :)
