Yes, the DSLReports FAQ on this is pretty-much the authoritative source.
If you have TV service, you CANNOT get rid of the Verizon router entirely.
And no, for the last time, you CANNOT connect a cable modem to the coax. It's not a cable signal, it's MOCA. You might want to research that term.
I must not have working TV at home, because I don't have the verizon router at all.
You have two seperate needs here.
1) If you want to connect to your ONT box and your only option is Coax, then you MUST use a MoCA WAN bridge. The Verizon FIOS router is able to do that. MOST MoCA bridges are LAN only, they will not WAN bridge. You'll have to look for specific WAN bridging ability (DSLReports has a somewhat dated, but good list of MoCA bridges and what they support).
2) Screw coax and run an ethernet cable to your ONT box and call verizon to have them switch the ONT Ethernet port on. Then you can completely ditch the verizon router, as you won't need a MoCA WAN bridge.
If you have TV service too, then ALL you need is a MoCA LAN bridge, which ALL MoCA bridges provide functionality for (WAN MoCA bridging is done at a different frequency than LAN bridging, which is why some don't support WAN bridging).
The four setups I've done are as follows:
1) Verizon router did it all. This got "boring" after a year or so of this, I moved to a new house and saw the oppotunity for change. TV, internet and phone worked fine.
2) I set the Verizon router in to Bridge only mode and rolled my own Netgear 3500L for about a year or so as a router, with the verizon router providing LAN and WAN briding. TV, phone and internet worked fine.
3) I wanted to ditch coax, so I ran a Cat5e cable across the unfinished portion of my basement, through a crawl space, up in to my garage attic and then down the otherside to my ONT box (phew, 120ft later, it's plugged in). I called Verizon, they rolled a technician because the person on the phone couldn't understand what I wanted exactly. Technician called me on the road to ask what it was I was looking for, they took care of it remotely before they even showed up...then confirmed that the ONT box was in Ethernet mode and left (no charge for the truck roll, I confirmed in advance). Verizon router still in bridge mode, but LAN bridging for my DVR only (it provides internet access for the DVR for guide and VOD ability. TV always works fine with no MoCA bridging/internet access). TV, internet and phone all worked fine.
4) I got tired of my Netgear 3500L, got a TP-Link WDR3600 and also shortly after ditched the Verizon router entirely and got an Actiontec ECB3500 MoCA bridge (LAN only bridging IIRC). TV, phone and Internet all work just fine.
The ONLY time you may need the verizon router to stay on your network is if you go with the option of "remote DVR" for Verizon, where that won't properly with their router not in operation on your network. So even TV subscribers are just fine without Verizon's router on your network, so long as you don't care about not being able to do remote DVR (IE accessing your DVR over the internet).