Of course they have. Off the top of my head examples include: Grants in the form of tax dollars (e.g. arxiv). To benefit the authors reputation (e.g. numerous scientists, developers, etc personal sites. zacklabe.com as a useful example). As a hobby (I think aiarena.net falls into this category). To collect data for research purposes (e.g. the original chatgpt release, and early recaptcha)...
Why would a government elected in a democracy be less trustworthy than a few private individuals? Do heads of large corporations not have an interest in controlling information?
It doesn't because it's not the Government funding it out of its own budget but rather the government forcing all citizens into an involuntary contract. This is really the worst possible combination of private and public media.
So let’s hypothetically say that some autocrat decided to take over Germany and decide a certain minority should be - I don’t know extinguished - wouldn’t a free non government run press be useful?