Cumulative update won't install (KB4571756) (Error 0x800f081f)

I don't believe there will be any "big update" until perhaps late Spring, 2021.

The next OS upgrade to Windows 10 Version 20H2 is only an "enablement package". Check out the description of this same type of Windows 10 upgrade that took place between versions 1903 and 1909 of Windows 10:

"Windows 10, versions 1903 and 1909 share a common core operating system and an identical set of system files. As a result, the new features in Windows 10, version 1909 were included in the recent monthly quality update for Windows 10, version 1903 (released October 8, 2019), but are currently in a dormant state. These new features will remain dormant until they are turned on using an enablement package, which is a small, quick-to-install “master switch” that simply activates the Windows 10, version 1909 features."

Version 20H2 of Windows 10 will soon become the current public build. Currently, Version 20H2 is available by joining the Windows Insider Program. The current 20H2 Insider build number is 19042.572. You may notice that this build number closely matches the current build number for the current public build: 19041.572.  The Cumulative Updates are the same for both 19041 and 19042. Both are at Cumulative Update KB4579311.

Based on reported successes that have been shared here, doing an "in-place upgrade" by downloading the current Windows 10 ISO, mounting that file in Windows, and running setup.exe has the most chance of success. By default, this will incorporate KB4579311 and the end result should be build number 19041.572.

Doing this after version 20H2 (build 19042.572) becomes public will probably have similar results, since both "share a common core operating system and an identical set of system files". The only difference is the "enablement package" that enables dormant features and changes the main build number from 19041 to 19042.

I don't want to reinstall the OS. I'll wait for this big update that everyone is saying is going to fix all of our problems.

After the in-place upgrade with the Media Creation Tool (as per the post by @TheHanna on page 15) everything was up-to-date on my PC. Today I got a notification that KB4579311 was available and it installed just fine without any errors. Have you tried that?

Thanks for sharing. Chatbot just repeated all stuff already known in this thread. Did not try to get a human on the phone yet... 

Stories about this not even being solved by a clean install or worse resulting in a broken windows makes me stick to the current working system without updates.

Based on my understanding. It seems to me that we have to wait until the 20H2 update is released or go for the media creation tool to solve it (which is not fully guaranteed that this method can entirely eliminate the problem).