>The spirit is good, but that software has cost good money to produce, and universities are dependent on external revenue
Obviously, but most of university research - at least in Europe - is funded by public money. The idea is that research funded by public money should be public by default, unless there's a reason to do otherwise.
>Also, should e.g. an American company have access to software produced by an Italian university?
Yes, of course.
Yet it's not American "public" money that funded it.
And it's good to realize what 'public' means in this case: paid for by the general public. What companies produce is also (often) paid for by them, only not via taxes but through purchases, subscriptions, etc. Why should the software produced by companies be exempt?