A piece of anecdata:

I've got comcast, and I recently bought my own cable modem because the provider given one was dropping packets.

To get it to connect at all, I needed to call them up and tell them the model number and the the MAC address (or something that seemed analogous) of the router. I had two models to choose from (fewer than usual because I needed DOCSIS 3 I think), and they made it very clear that these were the only models they would allow you to use.

(it almost goes without saying, despite using their business support, it took three or four days, most of which I was without usable internet)