The reading of Miranda rights doesn't in and of itself confer or trigger any new "rights". It's a reminder of the rights he already has. He could simply choos

The reading of Miranda rights doesn't in and of itself confer or trigger any new "rights". It's a reminder of the rights he already has. He could simply choose to not say anything without a lawyer being present and there's nothing law enforcement can do about it. People start talking even after being reminded, because I imagine for the most part, by now, those arrested think it's just a bunch of boilerplate that's part of the booking process - that it's almost a TV trope. Once read their rights, the police don't have to wait around for the arrestee to "lawyer up".