Intimate? Yes. Like one person talking to another.
Whether you are writing to hundreds or one person, it's the same. Your audience should always be thinking that you are in a conversation with them individually, not addressing the nation.
Lofty language such as, 'the public' or 'you, our valued customers', 'some of you may be thinking' or 'many people in the audience here today', makes people think they could leave or tune out and nobody would notice.
Even a slight change can suggest a conversation.
When Air New Zealand cabin crew say, 'Please turn your cellphones (plural) off', you know they're talking to the crowd. When they say 'Please turn your cellphone off'' you know they are talking to you. (Feel free to join my campaign to persuade them to change.)