I don't have to reboot my router or modem. I just have an a script that changes the MAC and releases and renews or rather gets an IP address via DHCP. My ISP is slow at handing out an IP address out as it takes several minutes, but it is automated. When the same operation is done for an IP on the LAN, it is a second or or two to get a new IP address.
I figure the main reason to get a new IP address is so that web sites can't track one by IP. If carrier grade NAT is used, then is there a point in changing one's IP?
If one does not use any peer to peer, then it seems that carrier grade NAT should lower the cost of one's internet service and that should be preferred. If one needs anonymity for bittorrent or other peer to peer, then shouldn't a VPN or i2p be used? I got the impression that i2p might be slow.