Anything local bypasses traversal of any network edges they can tap and monitor. Anything you ask Google is logged, and your search history can be subpoenaed, same as with any public library and the books you check out. OpenAI or whatever gatekeeper would assume that role and charge tolls.
Do the same research with Vicuna-13B-ggml or whatever and nobody can sniff out what you're doing. Which sounds great for people who just want to jerk off and be left alone, but has terrifying implications for anybody tasked with stopping more-malicious users.
Unfortunately nobody can ever compromise on these things. Best case would be adopting a law like the recent one in NL, where given probable cause the government can hack into your machine, but that won't happen. The only alternative in their favor is banning local models and open-source development of them altogether.