Hi all,
same problem here with Windows 10 Pro 20H2 (19042.662). The CCleaner installer does not install anything, the slim installer of the latest version 5.74.8198 does. MS Store was not the issue and only AV software is Defender.
Next problem after installation which went without errors: CCleaner does not start.
Nothing in the task manager, no errors at all. Double click does nothing. Windows sees the program as "incompatible". Maybe it is.
PS: I have used CCleaner for years and very regular.