If you mean some government should fund arXiv, specifically, then I don't disagree but would guess the government's default position of "it exists without public money, and we think that's rather excellent".

If you're suggesting it as alternative for academic publishing in general, it would cost a lot more.

Arxiv isn't a "publication platform" in the sense that peer-reviewed journals are. The cost of hosting and distributing PDFs is close to zero, obviously. What does cost money is the copyediting and running the peer review process.

People think Elsevier are the worst people in the world (not entirely wrong) and taking in millions while exploiting the free labor of authors and reviewers. But it's relatively easy to quantify the value they do add: their financials are public and, last I checked, they have operating margins of about 30 %.

Let's say we could do without their marketing and billing departments and that gets us to a margin of 50 %. That's pretty good, but it isn't quite the rip-off people sometimes suggest it is. Replacing the commercial publishers with government-funded open-access journals would be a billion-dollar endeavor, not a few million for servers and a bit of software.