DHCP can be set up to make things harder, but most people's IPs don't change very often. ISPs don't want to make it impossible to tell who had an IP address at

DHCP can be set up to make things harder, but most people's IPs don't change very often. ISPs don't want to make it impossible to tell who had an IP address at a given date/time because they need that information to fight other forms of internet abuse (spammers, phishers, hackers, malware, child porn, etc) as well as other legal requests they see from police and certain three letter agencies who file the proper paperwork with the ISPs legal department. This is generally a good thing and makes the internet a safer/better place. Any ISPs who made it impossible for themselves to tell which customer had an IP address is going to act as a safe haven for bad actors and they'll get blacklisted from many other networks pretty quickly. Only the largest ISPs can ignore abuse issues on their network without fear of being blacklisted and their IP space null routed.