My ISP no longer issues a new IP address upon router change. I'd probably have to go offline for at least a few hours or simultaneously change modem and router. In the meantime my household would notice, our phones would consume more of our cellular quota, my IP phone wouldn't ring, and even my thermostat would lose remote control functionality.

I'm not sure if it's the IPv4 shortage or copyright infringement/government surveillance pressure to maintain tight linkage between IP address, account, and legally liable person or address to raid.