The reason is simple, everyone can have a specific AI on their Computer/Server
Let’s take a couple of examples:
You have an AI specifically trained for your needs installed on your PC and you have to travel, with a normal App, you have to buy an internet connection for example on a plane and you always have to be careful about which Wifi you connect to so as not to risk your data ending up in unsafe hands, with the Local AI you can work completely offline, you can write a document and ask AI to verify it.
In another scenario, if you have doubts about processing your data, you can have a dedicated server in the office or on the cloud (with the appropriate security measures) and only your administrators can see the parameters and chats.