Re: phone numbers are easy
Taking file (NAS) and printing as examples, if you want to number your server or printer with a stable shorter address you already can.
fdff::a
would be a perfectly valid ULA if you want to have a LAN-only network prefix that does not need to change if you change ISPs.
(before anyone asks, yes in a large organisation your network operations team should remind you they follow guidance to generate a more unique /48 for the ULA to avoid conflicts if multiple organisations merge but I am talking about the self-contained and SOHO scenario).
And yes you can have your DHCPv6 service reserve fixed IPs for known systems whether or not you wanted to try to enter such an IP into a printer's control panel.
Your router may already provide ULAs alongside the globally routable addresses derived from a delegation from your ISP.
(Mine does and it is even a 3-way option of ULA never, always or enable only if ISP is down).
The link-local (fe80:whatever) addresses shown earlier are examples that you'd not normally use to reach operational systems and their closest equivalent IPv4 is 169.254.*
You'll see them auto-generated for each interface but never actually have to type those into a printer for example.
In addition to DNS, many LAN systems already use mDNS for discovery on the same network and you can replace the discovered IP with the friendly-name-of-device.local if supported to abstract from relying on a fixed IP.