Carlos, on FiOS, one can use their own router, but it can set up some limitations. The STBs get guide and VOD information via MOCA and the VZ-provided gateway is the bridge from Ethernet to COAX for that communication. (The primary STB can only be on COAX but the small, slave units in other rooms can be on Ethernet however) Some folks will use their own gateway/router for primary and just use the G1100 or Actontec gateway for bridging purposes. Some will invest in a dedicated MOCA bridge, but not many want to spend the money when they already have a device that can be used for this purpose in-hand. Further, if one wants to use certain mobility features, the Verizon provided gateway must be in the primary position, not behind a used provided gateway/router. These choices may become more difficult in the future as a recent testing phase for IPTV utilized a combination ONT/Gateway Router at the fiber demark. While that testing was discontinued and the IPTV shelved for the moment, the fact that they were testing a combination optical interface to the PON and router in the same device speaks loudly.
Folks on Comcat's XFinity may also have some limitations if they don't use the ISP-provided gateway.
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The most expensive tool is the one you buy "cheaply" and often...