Sure - but with most of the same caveats that apply to moving your own globally public IPv4 address around... ie, you need to register for an AS number, buy the IP space you want, and publish routes in the global internet routing table.

Its nowhere near as cheap as DNS and much more complicated (since you're concerned about things like how, physically, pulses on a wire/fiber will make it to the edge of your network.. you need to peer with one or more ISPs).

You could lease address space from an ISP and make all of that their problem, but then of course its not _your_ IP space. Think of it like the difference between being an internet user (leasing IP space) and a member of the internet (running your own network).

Since we're specifically talking about DNS in here though, I really don't think a stable IPv6 address would be a viable alternative to what we use DNS for.