This is something we spent a lot of time considering, and ultimately I do not agree that it would be better the way you are suggesting.
If cards that died in survival mode could still be used in other formats, then it is effectively forcing everyone who currently plays in modern and wild to also play in survival mode or else they are losing out on rewards they could otherwise be earning.
This is similar reasoning for why energy is not separate between modern and wild format which I believe is working well there. It's important to understand that this new mode is not expected to be for everyone. This is specifically geared towards players with large collections including multiples of many cards and we expect most players that don't fall in that category to stick to modern or wild format.
RE: Introducing Splinterlands Survival Mode