How is it not easy to discover? You flip the switch, the phone buzzes and shows you what happened. It's one of the few buttons on the phone, it's not like it's hard to find. Not to mention contextually it's right next to the volume buttons which is where it should be.
When you do that it has a big crossed out bell, which worries you the alarm isn't going to go. I never sleep well if I have an early flight as I'm never 100% sure I haven't silenced the alarm!
I'm pretty sure it's literally impossible to silence the alarm from the built-in Clock app on iOS. Third party apps are subject to the usual notification settings, though.
(Not to mention that the mute switch has been consistently implemented on 100% of iPhones since the first model in 2007...)