alt Hacker NewsI would in fact guess that it's not common at all. Setting up your own cable modem and router is going to be intimidating for the average consumer, and the ISP's answer to any problems is going to be "use our box instead" and they don't want to be on their own that way. I don't know anyone outside of people who work in IT who runs their own home router, and even many of them just prefer to let the ISP take care of it.
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Common no, very easy to proliferate though as people become aware of the savings possible. And the 2 cases I've seen where litteraly order the same model online and swap it, no configuring required. And it wasn't even the family tech support guy(me) who came up with the idea. The ISPs incuding the router as a monthly line item on the bill are litteraly indirectly asking you to do this.
I think it is less common now, but ISP routers on average used to be trash with issues — bufferbloat, memory leaks, crashes — so a number of people bought a higher end router to replace the ISP provided one. Mostly tech savvy people who were not necessarily in IT.
Nowadays my ISP just uses dhcp to assign the router an address so you can plug any box into it which talks ethernet and respects dhcp leases to be a router which is nice, albiet 99.9% of people probably leave the router alone.