Sure, they can, but they won't bother. The average American isn't going to download software on a PC. They have an iPhone or Android device as their primary computer. Banning the app stores is enough to get the manipulation of the masses that they want.
From what I understand, China does the same. Ban the easy things, only bother to crackdown on the harder things (like VPN or cryptocurrency) when they start to get out of control.