Domain Name vs IP "discussion"

I'm having issues with a network guy that is take over my role as networking "guru". I'm a developer and I don't tend to remember a bunch of IPs, so when I set up the network, I had a very easy to remember naming scheme "dyndns-hostname:modelNumber" where the last digit was a serial addition to the model number. For example the ssh on 3 Dell R210s we have are:
dyndns-hostname:21220
dyndns-hostname:21221
dyndns-hostname:21222

I also set up DHCP reservation instead of static IPs, because I'm a developer, I don't go mucking about setting up LAN DNS servers.

So now, when trying to access web ports - you guessed it "dyndns-hostname2180[0-2]" - I can't connection. His response: "Don't do a u-turn, use the IP."

As far as I'm concerned, that's equivalent to looking someone up in the phone book by their phone number. He has a LAN DNS but he won't add entries.

I've always used dyndns regardless if I'm local or remote, I don't understand why he's against this. Are there any resources I can read to support his network dictatorship?