This seems like an approach that requires a national or international level collaborative organization. Having every LAM contact a vendor for legal copies is redundant. What would be better is having a single organization obtain the licenses or having that organization negotiate with vendors to provide an easy method for LAMs to obtain software.
In the first method, the collection National Software Reference Library at the National Institute of Standards and Technology would be a good starting point. As it stands, their collection is probably one of the largest, but it is used to match against programs on computers used in crimes, not to serve as a general resource for researchers. It would be great to use that collection to seed a general resource, but the licensing for use (the very hard part) would still have to be sorted out.
In the second method, organizations like Techsoup show that this group negotiation model is possible with commercial software.