If the FO is PM, he'll just tune VHF1 or 2 on RMP2. If the CA is using the radio he'll tune VHF1 or 2 on RMP1.
The unwritten SOP is that you use your own panel. I guess you could use the offside RMP, but the other pilot would look at you and say "we don't do that on this fleet" 😊
The SEL light is on 99% of the time.
I understand the seriousness of the lost communication scenario that you mentioned, but SOP is VHF 2 on 121.5 unless it's needed for something else. That ought to prevent that sort of incident.
As an aside, I've noticed here in the US, Boeing crews hardly ever tune offside, while Airbus crews do it all the time. The last time I asked a Boeing crew about that, they gave me a funny look, as though the thought had never occurred to them. They eventually admitted that it "should be possible".