Insecurity leads to loss of privacy, but security does not lead to privacy. Things can be secure and non-private by design.

Sometimes, but sometimes security measures lead to less privacy. Say, if executing local programs sends information to a remote server.

If that information can’t be used to identify anyone then it retains privacy while being secure. Being slow would still be an issue.

But you can't be 100% sure that the server where the information is sent is not putting in a database your IP, the app you run and whatever else. As a power user I would prefer a prompt before anything is sent.