It doesn’t have to be. 
For example, Apple’s HomeKit uses either WiFi or Bluetooth as the communication Protocol and everything runs locally except Voice control. The individual devices may have their own clouds for their own apps, but HomeKit doesn’t use that pathway.
The new Project CHIP which Amazon, Apple, Google, Samsung, the Zigbee Alliance and others are participating is intended to create a standard home automation profile for IP addressable devices (including WiFi devices) so that devices using that profile can easily communicate with each other and with the Big Three voice assistants (Alexa, Google Assistant, and Siri). Although most of the voice assistant work won’t be local, an extra benefit will be that this should enable local operation similar to HomeKit’s for automations and potentially even app control.
Matter - smart home connectivity standard (formerly Project CHIP)