L and T have never made me wait due to a previous client having an emergency. Even for me, if I'm in a crisis and they don't have time for a double session, they're able to calm me down before time's up. I've left sessions crying. I respect that they have to do that. I don't want another client intruding on my time, so why should I feel like I can intrude on theirs. Though it does suck having to leave upset.