Absolutely! Using open source software is much cheaper, as well. Hiring developers to work on open source software/OSs would cost less than buying software annually. Governments pay stupid amounts of money for easily replaceable software.
It would be nice if governments could make a "software union", pledging to use the same standards. It seems that everyone is inventing the wheel separately in every country or falling back on commercial industry standards.
F.i. the exchange of financial documents. There's a standard coming along called SAF-T, and even if it is a standard, every country using it are making their own definitions of what it is. There are also some countries that already have their own completely different standard. The crazy thing is that almost every country worldwide are asking for the exact same info on tax returns, but they've all individually come up with that. Only differences is the order of fields on the form.
Same with user identification. Every country has their own almost identical solution for identification, which however does not work across borders, despite the similarities.