I think that's a poor application of tragedy of the commons.
Also, in your example, I don't know how other cities' use would impede the funding city's use.
Also, in your example, I don't know how other cities' use would impede the funding city's use.
If the lab has to give the software away, all development ends, unless you have $300k/year of grants sitting around.
If they can't get the interested labs to contribute towards the development without the coercion of a commercial license then it sounds like it's either done, or the development roadmap is misaligned with the users' goals. In either case, stopping the abusive current practices would be an immediate improvement for everyone involved.