Well, technically a Host isn't on a grid, and devices slaved to that host are likewise functioning on the host, not a particular grid. It's a little "wibbly wobbly" how that works really. Hosts don't exist in any particular location (they exist everywhere) so it's a little weird.
As far as bringing the Signal Rating goes, I can appreciate the interest, but I think more effort in improving the way Noise vs. distance functions would be easier and more appropriate. When they revamped the way the Matrix functions, they took the concept of connection hopping (mutual signal range through a series of devices from 4th edition) and simplified the process. Now, the idea of hopping from device to device is unnecessary because everything relays everything. That's why it is called the Grid, it functions as a Mesh network and everything communicates. Hacking in 5th edition is more about grabbing permissions for yourself to access the actual devices and their functions. Noise (from distance) is the replacement for Signal, resulting in the idea that the further away your are trying to communicate the more interference you're going to get. Personally, I think this is a decent replacement than the idea that you need to hack Node after Node to gain access to some far off system.
Now, as far as things go for having certain devices function without connecting to the grids, it is technically possible, but that is functionally the same as going wireless off. The Grids are your connection to the Matrix, you'll lose the wireless bonuses (i.e. the Smartlink bonus to dice pool) because you aren't getting the Matrix mesh network data and extra processing. If your GM wants to allow devices to effectively function at the 4th edition "Signal 0" where they could communicate over an extremely short distance but don't communicate with anything else, that seems reasonable to me. It's effectively the same as just using wires to connect everything.