Why does academia still use scientific journals and not peer-reviewed government funded alternatives? ------ NOTICE ------
The above put box &quot;This question already has answers here:  Why are journals used in modern scientific academic research?&quot; is wrong and void: it has a title that sounds similar to my question but the question goes into Arxiv and the answers are in regard to Arxiv (&quot;Arxiv is not peer reviewed&quot;) which is not the issue discussed here. The question here is why &quot;peer-reviewed government funded alternatives&quot; are not used.

The field of science is under-funded but we follow a publication system that has two major (expensive) options for publishing:

Paywall journals: Scientists do the science and write the papers
(using mainly tax money). Scientists act as editors and reviewers
check the quality (while paid with more tax money). Once years of
work have gone into a paper the journal takes it without paying the
authors, academic editors and/or reviewers a single cent and puts
the paper behind a paywall. Now universities have to pay the journal
huge amounts of money (exact numbers are usually not available due to NDAs) to access the paper to which the journal did
not contribute anything (apart from minor formatting issues and
putting a pdf on a webpage maybe).
Open access journals: Same as above (scientists do all the work) but
authors even pay the journal a substantial amount of money which can
easily go up to 6000 USD in &quot;respected&quot; journals (I am not talking
about predatory open-access journals here – the 6k is for example
for the journals of the American Chemical Society which publishes a
few of the leading journals in our field). For this amount of money
the journals do the minor formatting issues mentioned above and
upload a pdf on their webpage. There is just no relation between
their fees and what they do for it. Here 60-100 USD would be more appropriate than 6000 USD.

Is this not fundamentally wrong that scientists do the work and journals skim off the profit? Why do scientists (and tax payers!) still put up with this?
I do understand that historically :

Journals made sense as someone needed to print the
articles into books to make them accessible to everybody and
layouting might have been something non-trivial but nowadays this is
not the case any-more.
Scientists have brought themselves into a dead-lock due to a
publish (in high impact and &quot;respected&quot; journals)    or perish in
which you have to publish in certain journals in order    to be seen
as a good scientist.

But would it not make much more sense to have tax-money funded    web-portals that use editors and reviewers to assess quality of    articles and make them available for download as journals do it currently? That would cost a fraction of    the paywall and open access fees that journals make money from at the    moment.
Why does science still stick with journals? My feeling is that the field of science does not need the journals at all anymore - what am I missing here? I have never really gotten a satisfactory answer from other scientists (mostly things like &quot;this is how things are and we can not change them&quot;) therefore I am asking here  ...
There are many businesses which are inefficient in the sense that you judge publishing by. There is nothing requiring markets to accomplish some collective endeavor efficiently. Instead, markets are only efficient in terms of people being able to pay for things they want. For example, whether avocado toast is good nutrition is irrelevant to the market. But if you want to pay $15 for it, and if there is someone else willing to give you an avocado toast for $15, the market will certainly provide for that exchange.
Likewise, your arguments about how the current publishing system is inefficient are tangential at best. It so happens that a lot of people (in the current world, not in some fantasy post-journal world) want to publish in journals, and read what is published in journals, which is why the journals exist. You point out some important reasons for this and say you understand this, but

would it not make much more sense to have tax-money funded web-portals

Well, no, it wouldn't. If there is demand for service A, why would the market fail to supply A and instead supply only service B which doesn't fill the same needs? The answer is that a free market wouldn't. You could have government force the market to not provide service A and only service B, but then you have a non-free market. Which isn't the end of the world, but it so happens that most people in charge of government these days favor free markets, barring corruption.
That's the most direct answer to your question: The current publishing system is in place because that's what the free market came up with, and implementing your system would require government interference in the market. It is not politically expedient to implement such interference. This is all for today, mind. 20 years ago open access was a pipe dream, perhaps 20 years later publishing will change completely. But we can only speculate about the attitudes of the future.

I'd also like to point out some inaccuracies in your question.

Scientists act as editors and reviewers check the quality (while paid with more tax money)

Actually editors often get paid by journals. Also, not all research is publicly funded.

Now universities have to pay the journal huge amounts of money (exact numbers are usually not available due to NDAs) to access the paper to which the journal did not contribute anything (apart from minor formatting issues and putting a pdf on a webpage maybe)

These days, a lot of research is made freely available after a few years, the university is really paying for quick access (and also access to very old papers).

Here 60-100 USD would be more appropriate than 6000 USD.

No, it wouldn't be, because no journal would bother. $60-100 USD would buy you maybe 1-2 hours of work from a single skilled person in which they must:

Read the manuscript
Finding reviewers and keep bugging them to submit reviews on time
Read reviews and decide if they make sense, then pass them on to the author
When revised MS is in, work with reviewers to decide if the revisions address the initial concerns
Work with authors to get it formatted and proofread

It is not realistic for a single person to do a single one of these in a few hours, much less all of them.

Is this not fundamentally wrong that scientists do the work and journals skim off the profit?

There's nothing more wrong than any other for-profit enterprise. The only thing you can criticize here is the entire concept of seeking profit, but I don't believe there are currently significant contributors to science that are opposed to profit seeking. The closest thing that comes to mind is China, but they have for profit journals also, and a lot of Chinese research is published in western, evil capitalist, journals anyway. Now that you mention it, when the USSR was around I think they did have government run, non-profit journals.  But it is not considered &quot;fundamentally wrong&quot; by most governments today.

make them accessible to everybody and layouting might have been something non-trivial but nowadays this is not the case any-more.

No, it is easier, but still non-trivial. Even just writing a manuscript purely for yourself takes some work to get all the equations, figures, citations and so on to display correctly. But if you had a journal where you want a uniform formatting from many articles by many different authors, it is a lot of work to come up with a system that works for everybody and also get the authors to follow it.

That would cost a fraction of the paywall and open access fees that journals make money from at the moment.

Government can be notoriously wasteful, so it's not a given that it would be cheaper. Perhaps the cost might be spread out over everyone via taxes, instead of being born by individual universities, researchers and those poor souls who actually pay $30 to download a PDF. But then the first two are already covered by tax money.
You have to also consider quality of service and not just cost. The classic US example of government-provided service is the DMV. It doesn't make sense to be a realist on private publishing and an optimist on public publishing.

My feeling is that the field of science does not need the journals at all anymore - what am I missing here?

Well, I suppose we can say you are missing the trees for the forest. Science is not a single person. Individual scientists obviously do need journals. Nowadays, thanks to the internet, they don't need them to publish - but they still need the credibility of being peer-reviewed and the visibility of being in a highly-read journal. They also need them for the mundane reasons of justifying job and grant applications.