There are many issues with dynamic IPs for stations providing services such as web, email, FTP, etc.

• Can’t guarantee they’ll always keep the same IP.
• Changes need to be reflected on the DNS, which may have been set so that hosts can automatically register themselves or not. DNS changes take time to be propagated to other servers.
• Some applications need the IPs to be coded within them, if the IP is changed it has to be reflected as well.
• Most importantly, when you configure the firewall, it’s for that specific IP, I personally haven’t seen a firewall where the host is configured with name only and DNS is used to lookup the IP.

• For email, services, PTR records are created to verify that you are not a spammer and if you don’t own your IP block, you got it through an ISP which is the common case, PTR records for your IP block is pointed at their main DNS servers and not yours. So imagine the headache of everytime calling your ISP to change the public IP record. You may argue well only the private IPs are changed and mapped to the same public IP, you’d be amazed to know that some configure their public IPs direct on their servers.
• DNS servers are configured with IPs only. Example, if you are looking for x.google.com, a list of their DNS IP addresses is added (ex: 216.239.32.10) in other root DNS servers for you to go there and retrieve the correct IP.

That’s what I came up with, there may be other reasons