Yes, I'm sure your "local AI" running on 8 gb of ram will be able to filter the ads added by the super computer AI just fine.
• Small models have performed really well in recent years. • Newer phones will have more RAM. • Private LLMs do not necessarily need to run locally.
LLMs cannot act on encrypted information - the server must have access to all your plaintext prompts. And you simply are forced to trust they don't keep them forever, but they probably do.