Maybe it is possible to add apps to whitelist in a future? 
I saw this implementation in Sony Xperia. I will explain why. Now I am using SGS4 I9505 running 4.4.2. I have Google Play Music Unlimited subscription. So, I am listening music with streaming option, screen goes off and after some time avast! Battery Saver turns off my data connection and no music left. I know, the option is to turn off Battery Saver, but it is so inconvenient… ;D
Hi =YLAP=,
we know this is an issue. Right now we try to check if there’s a data traffic on the network before switching it off, but different music streaming apps have different cache sizes etc., so it doesn’t always work. We plan to fix it in a similar manner to what you propose, we just need to find some time to do it 
Ondra
Maybe you could give an option to exclude network traffic from saver plan?
Not sure what you mean Nefrekedyzer. Could you please elaborate a bit more? Thanks.