This is not really an end-user issue but it is a serious usability issue for IT admins and developers. It's very very common to schlep around raw IPs constantly when messing with networks and I don't see that going away. It's also very important to be able to visually parse IPs when understanding the topology of a network, writing firewall rules or routes, etc.
This is a DX (developer experience) issue more than a UX (user experience) issue.
Edit: three specific problems with DNS:
(1) What happens when things are not configured yet?
(2) OSes are designed to have one DNS server but people belong to many networks either at once (local + VPN + virtual + ...) or serially via mobility. In reality you need many DNS servers, but then how do you deal with naming conflicts?
(3) DNS is dependent on IP so you can't use DNS to debug DNS issues. It's a circular dependency.
In practice IP schlep is very common.
I mean DDNS where the DHCP server tells the DNS server which IP has what hostname, not e.g. dyndns.
Actually that's not a problem for that. Since people who are actually using them have no idea about IPv4, too and just copy addresses. Actually you could create local address with everything prefixed by fd + 40 bit which could be just fdff:ffff:ffff:ffff::1 which isn't really hard to remember.
On the other hand, DNS could fix this - just have a TLD of ip6 and have it resolve all the examples in the article. It would require no changes to current software and will work transparently. I.e. you'd enter http://deadbeef.ip6:1234 and when the ip6 TLD servers receive a request for deadbeef.ip6, they will reply with dead:beef:0:0:0:0:0:0. Similarly with deadbeef.1.ip6 and so on. You could easily implement this in the OS too without much hassle and not even need servers on the internet to do it.
http://deadbeed.ip6 would help to start using it.
If the local dns could be setup to autotranslate them to ip6 could help this notation to gain traction
I just had this dystopian vision where a non-profit operated .ip6 to work as discussed then went defunct and a domain-grabber (named Network Solutions) bought it. Everybody scrambled to patch their recursive resolvers real fast :-)
In any case, if you really need to, what's the problem with copy-pasting an address?
In an embedded system where memory is at a premium and you may have serious constraints on how long things take (e.g. for timing purposes), the ability to hard-code an address or have it entered in some way saves you from having to support an entire DNS layer in that system.