I think it depends. The OS provides an API signal -- presumably that websites can access. So if a site decides you're lying, what happens then? For instance, 100% of bots and malicious actors will lie, unless they think they can get what they need by being a child.
And some adults will lie too, assuming they don't need adult content, to avoid being tracked for advertisements, if laws exist that prevent ad targetting on some demo, say <13 year Olds.