HomeKit works great as long as you have devices that support it. The only thing you need a server for is if you want to be able to control things while you're away from home. Control/notification on the LAN is entirely local. Setup for non-technical users is easier, too. You scan a code through a standardized flow, rather than downloading Yet Another App and creating Yet Another Account you'll forget the password to.

Being tied to the internet happens because manufacturers want to be able to watch your usage, sell you ads, and make you buy more stuff from them when they decided your existing hardware is "too old" and shouldn't be supported anymore.