I think the problem is that there are so many aircraft airborne these days, and ATC sectors have been combined; that VHF ATC comms are becoming so busy (in Europe) that in some regions there can be near constant chatter on Box 1. Add to this the conversations on 121.5 between old mates and it becomes unmanageable at times.
In just the last week, I missed calls three times from Box 1 because they were 'stepped on' in my headset by stations on 121.5. I think I will have to start putting in ASR's about this.
Sometimes one has to actually turn off 121.5, but then of course how do you remember to switch it back on?
As an ex communications engineer, I like "personfromporlock's" idea of a temporary mute button: A non-locking button that you pressed which would mute box 2 for, say, one minute.