[…] a public institution is really not a great example of the general population […]
Which I touched upon in my disclaimer, but in some ways it is a great example. Public institutions are defined by the general population, indirectly through their representatives creating the rules that govern them, and directly through contact with the public at large. Now if all our institutions still use this very outdated technology, and you can have trouble convincing them - during a global pandemic mind you - that using email is just as safe as using fax (so not safe at all basically), then that speaks to a larger mindset in the general population.
Many in the general public are also a lot quicker, some might even say careless, with adopting new technology of course. But as a society we are rather slow, and there are surprisingly many individuals who are hesitant or entirely resistant to adopting new technology. The fediverse usage is a bubble in a bubble here.
The internet infrastructure is another good example for this on the societal level, as there were plans in the 1980ies [!] to lay out a glass fibre network between every publicly used building in the country, which would have gotten us a good part of the way towards adopting this new material at scale. But in the end it was deemed unnecessary and too expensive and the project got canned (mixed in with rumours of “close friendship” between the chancellor and a major copper producer). Instead now we have people running around thirty years later and collecting signatures at the door for last-mile fibre network projects that seldom make quorum and thus almost never materialise public funding.
Both of these options have their pros and cons, and I think it is important to explain these well to the council if you want to have any hope of convincing them.
A line of argument that has had some success in Europe is what has become known as “Digital Sovereignty”, basically a fancy term for saying government should control its own infrastructure. So you might want to sell it as an easy way to have a permanent archive of public communication and a method for it that is under their direct control, rather than as a way to find more engagement.
As others have said self hosting has a maintenance and moderation overhead, but this can be lessened by running an instance together with other cities while still retaining most of the benefits of self hosting.
Seeing from the linked cross-post that this is about Port Alberni, and considering that http://portalberni.ca/ returns an empty reply while https://portalberni.ca/ lets me know I have been geoblocked because I’m outside of Canada and the US, I’d say you have an uphill battle before you though. These people made a website (probably paid for it, too), and then killed much of its use by geoblocking most of the world.
Good luck.