No ISPs use static unless you request it (or it's part of the service, typically premium). The only reason you'd ever need a static IP is if you're running some form of service (Like a web or mail server) which needs to resolve to the same IP when people/devices look for it.
If every single router needed to be statically assigned an IP address it'd be an absolute nightmare to manage. Hell, even in private domains you use a DHCP server for maybe a few hundred clients. An ISP would be dealing with a few hundred thousand clients if not millions, if in larger countries (say, America).