You wouldn't want an alarm, you forgot, to go off during a funeral. Many people use alarms as reminders.
Applications that ignore the mute button are not only games. Runkeeper, Jamie Oliver cooking, etc.
Which ever way you turn it, it is just silly that a mute button only mutes some applications.
Poor application design. If the devs don't support muting the app then it's on their shoulders and they should be the ones you complain to. Also, you can mute and turn the volume down all the way, or just turn off the phone (which a funeral would probably warrant).