Anyhow. The justification is that it is an important part of a communications infrastructure.
Just like the government finances roads, etc.
Politics is also about making practical choices to advance humanity.
Such a weird comparison. Just so we are tuned in, can you list some things that are of less value to you than a single bomb on a stranger?
I just really don't like my government killing people far away that pose no threat to me.
Because the government should provide useful services. It should be funded by tax dollars because I'm tried of libertarians, and it's well-demonstrated that the free market has consumer hostile incentives that I'm sick of.
Your assuming the local government employed webmaster won't favor his friends restaurants.
Craigslist basically is this, and it's more or less free.
Oh my! Mic drop! You got me! Corporate owned sites would have to be unbiased, right? It's not like a business would ever do something as disreputable favoring a restaurant that paid for the favored treatment, or try to steer you to affiliated businesses. Inconceivable!
But seriously now: a government-run site would be way better and have less biases. In the US, there's a good chance it'd be run by civically-minded people, and there's about zero chance that conflict of interest would be baked into its "business" model.