Implications of modems
Since LibreWRT came to my attention, I've considered buying a router compatible with it. This got me to thinking, however, that the router is connected to the modem and as far as I know there's no way to free a modem. Is this not a big concern? It seems to me that from a network security point of view, the modem would be a single point of failure (if it had a backdoor).
As one of the people working on LibreWRT I can say that we'd love to support a modem. If anyone would like to help with that, please visit librewrt.org. The first step is probably to identify a good candidate modem.
It's just like any other router between your LibreWRT router and any
remote host you communicate with. It is a single point of failure: it
can e.g. overheat and make your connection less reliable. Unless your
network does generally insecure things, its backdoors shouldn't do more
than disable the device or drop some packets.
I too want to get a router that runs a free distribution. Unfortunately, my current router (Netgear WNDR3400) I don't think can run a fully free distribution, but I do have it running DD-WRT.
I think I can have it running OpenWRT however, and I might consider doing that instead.
I once read about mikrotik network devices that use Router OS which is a
variation of gnu/linux but may be the hardware isn't much free I think.
That plus, bets are Router OS comes with a good deal of proprietary software, regardless of being based on GNU/Linux.