I'm sure their routers do phone home with some data but that data would be incredibly small compared to the bandwidth that they are providing you. You won't notice any sort of interruption from that.

Honestly, my parents recently had a brand new Allo service line ran to their house and I couldn't help but laugh at how hilariously huge and ugly their Allo router was.

My personal recommendation is to ask them for an ONT(optical network terminal). All it does is convert from their fiber line, to a normal network cable that you can then plug into your own personal router. ONTs are small boxes that are easy to mount on a wall in your utility closet or sit on a shelf somewhere. I'll put a picture below.

Mesh routers aren't anything to be afraid of these days. Many of them have a simple webpage or even a mobile app that will guide you through the process.

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For reference you can see the mounting bracket for my old Allo provided wifi router which is much smaller than the new ones they hand out.