iOS is still useful without an iCloud account. Everything still works. Calendar, Calculator, Contacts, Safari, Music, etc, on and on all work just fine. You can add any number of third party services with the email app. All you loose not logging into iCloud is sync'ing of said data to other devices. It's a local only device at that point.

Pretty sure the same stands for Android.

The Windows Store (now called the Microsoft Store, apparently to match the name o their physical stores), does allow one yo download free programs without using a Microsoft Account. I'm guessing you might need one for paid programs, but I've literally never tried, since this is a PC, not a phone/tablet.