Everything is supposed to fall back into public domain, even old videogames and movies, but these items can easily be lost over the years because preservation effors are usually done by piracy websites.

Because few films are in the public domain and even fewer (none?) videogames are. A situation that becomes worse by both the copyright length differing between countries and Disney's lobbying efforts comically extending said length. As a result, your best bet is piracy or the Internet Archive.

Well, for one:

Public domain is legally defined by different countries.

For Two, try looking before asking.

In Germany we have a Computer Game Museum which is doing software preservation:

https://www.computerspielemuseum.de/1210_Home.htm
https://www.computerspielemuseum.de/1282_About_us.htm

As you can see, it is sponsered by the EU and Berlin and they are part of a project which is funded by the Federal Ministry of Education and Research.

Ah, but they don't have video games and movies, do they?

Well, why don't you set up one? Because it takes effort and money to make it happen and keep it up?

I think archive.org is supposed to be a bit like that though, but the whole site seems... kinda messy. Not very organized IMHO.

One valid question is should there be some central main servers keeping all the data, or should it be dispersed all over the world like bittorrent? Then the costs to keep up to servers could be kept to the minimum. I think archive.org has arcade (MAME) games at least, if I recall correctly.

No, because the legalities of public domain put the burden on the government to retain items for public domain. Archive.org is a piracy website, they don't really count. I mean official as in government sponsored, not just a random piracy website that will die as time passes.

I don't think its intention is to be a piracy site, but pretty much what you asked for.

Which government should sponsor or establish such website? US government? Would they be allowed to keep only US-originated movies and video games? Would people from all over the world be able to access it, or only US citizens?

IP rights are nonexistent when it's for archival or educational purposes.

It is really unhelpful for these ip obsessed ignorant chimps to be going on about ip rights.

They're not nonexistent as such but there typically are specific legal exemptions.

Archive.org's funders include the US Federal Communications Commission and National Endowment for the Humanities, so in that sense it is, in fact, government-sponsored.

A funny kind of 'piracy' site that implements Controlled Digital Lending, though there was that incident during the pandemic: https://en.wikipedia.org/wiki/Internet_Archive#National_Emergency_Library

Probably because 99%+ of all the material that is in the public domain is total garbage that no one cares about, unless you are talking about old literature from before the 1900's.

Who does? There's so few in the public domain?

Library of Congress, maybe?

There are no limitations for this kind of thing. Stop pretending otherwise.

If all you can do is accuse me of lying, I have no reason to engage further. People can conduct their own research (and should seek appropriate training if they actually intend to do archival or educational work).