How can access on an android device be restricted to applications or widgets on the home screen only?
It turned out that there's a solution without using additional apps, at least on 4.4.4.

Settings -> Users -> Add user or profile -> Restricted profile.

From there, it's just like an app locker, where the apps that should be accessible are turned on. Once the restricted profile is active, the apps that are not active are just not visible in the apps list.

The best thing about about this is that it's a built-in solution that doesn't require questionable permissions granted to an app.

Negatives: the main settings app can't be restricted for some reason and the system apps that are supposedly disabled, suddenly become active, which is particularly bad as the description for the feature says that it restricts access to apps from your account, so you'd have to do it all over again.

Advanced: Restrict Me module for Xposed is supposed to enable turning off settings as well. Not tested.