I think there are many thousands if not tens of thousands of WP installations. If there was such a fundamental flaw I think it would show by now. If only .5% had some form of error it would still look like a lot of sites, indeed it would be a lot, but not compared to how many work OK.
I am suggesting that there could be other issues regarding the WP upload. Often there are errors using the /tmp directory set in PHP. You, as a user, might have permission issues and so on.
Hosting companies will try briefly to do what they can, but they have their own agenda as well. All I was suggesting is that you should try running a simple file transfer using a .php file outside of WP and see if it works. If you can't do this then maybe the techies at your web hosting can do it as a test on your behalf.
WP should work straight from the uzip file, but depending on so many factors it doesn't always. I can't help you as I can't access your host, so if there are checks and changes that are needed you are the only one who can do that. The alternative is to find a developer who can help and pay the appropriate rate, or keep asking your hosting to check out what is going wrong. Running a test upload is hardly going to them more than a few minutes for them. Normally I would suggest running phpinfo and checking the /tmp directory, but that might be best done by them as well.