Some streaming box do have built-in smb server or allow certain app to run as smb server. Just attach any usb storage device to the usb port, you'll get simple network attached storage (NAS).

For example, nvidia shield do have built-in smbv3 server, that allow any usb external storage that is connected to the usb port, to be accessible by any device within the same local network via wired/wireless. So in this case 1Gbps lan is really useful to speed up the transfer time compare to 100Mbps, especially when you're transfering huge files from it and vice-versa.

However, if you just use the streaming box only for streaming purposes, 100Mbps is more than enough even to stream 4k video. Infact, netflix only recommend 25Mbps for their UHD content