I am a pretty big fan of Open Source and have used Linux myself since the early 90’s. Most governments are not going to save money switching to Open Source. At least not within say the term of a politician or an election cycle. Probably the opposite.
This kind of significant shift costs money. Training costs. Consultants. Perhaps hardware. It would not be at all surprising if there are custom software solutions in place that need to be replaced. The dependencies and complexities may be significant.
There are quite likely to be savings over the longer term. The payback may take longer than you think though.
I DO believe governments should adopt Open Source. Not just for cost through. One reason is control and a reduction of influence ( corruption ). Another is so that public investment results in a public good. Custom solutions could more often be community contributions.
The greatest savings over time may actually be a reduction in forced upgrades on vendor driven timelines. Open Source solutions that are working do not always need investment. The investment could be in keeping it compatible longer. At the same time, it is also more economic to keep Open Source up to date. Again, it is more about control.
Where there may be significant cost savings is a reduction in the high costs of “everything as a service” product models.
Much more important than Open Source ( for government ) are open formats. First, if the government uses proprietary software, they expect the public to use it as well and that should not be a requirement. Closed formats can lead to restrictions on what can be built on top of these formats and these restrictions need to be eliminated as well. Finally, open formats are much, much more likely to be usable in the future. There is no guarantee that anything held in any closed format can be retrieved in the future, even if the companies that produced them still exist. Can even Microsoft read MultiPlan documents these days? How far back can PageMaker files be read? Some government somewhere is sitting on multimedia CD projects that can no longer be decoded.
What about in-house systems that were written in proprietary languages or on top of proprietary databases? What about audio or video in a proprietary format? Even if the original software is available, it may not run on a modern OS. Perhaps the OS needed is no longer available. Maybe you have the OS too but licenses cannot be purchased.
Content and information in the public record has to remain available to the public.
The most important step is demanding LibreOffice ( or other open ) formats, AV1, Opus, and AVIF. For any custom software, it needs to be possible to build it with open compilers and tools. Web pages need to follow open standards. Archival and compression formats need to be open.
After all that, Open Source software ( including the OS ) would be nice. It bothers me less though. At that lobby, it is more about ROI and Total Cost of Ownership. Sometimes, proprietary software will still make sense.
Most proprietary suppliers actually do stuff for the fees they charge. Are governments going to be able to support their Open Source solutions? Do they have the expertise? Can they manage the risks? Consultants and integrators may be more available, better skilled, amd less expensive on proprietary systems. Even the hiring process can be more difficult as local colleges and other employers are producing employees with expertise in proprietary solutions but maybe not the Open Source alternatives. There is a cost for governments to take a different path from private enterprise. How do you quantify those costs?
Anyway, the path to Open Source may not be as obvious, easy, or inexpensive as you think. It is a good longer term goal though and we should be making progress towards it.