> It could be a UUID v7 stacked on top of another UUID v7 for all I care but it would be globally unique and available free of cost.
You're essentially talking about IPv6 addresses.
Interestingly, most residential ISPs these days already issue your home network an IPv6 /64 or better! But they (sadly) just firewall off use of most ports that residential users have no purpose for — on my own network, even if I configure my router to allocate each machine on the network a public-routable IPv6 address, the only port the network (not the router!) is willing to allow non-established incoming flows to is 22/tcp.
But even if they worked, they'd still be ephemeral. At best, even if your ISP keeps the allocation the same, you'd lose it if/when you switch ISPs. (Similar problem to ISP email addresses.)
The real key here, would be if someone was freely giving out tiny slices of IPv6 https://en.wikipedia.org/wiki/Provider-independent_address_s... to individuals; and there were hosting providers / residential ISPs willing to add BGP routes in their ASN for these tiny prefixes. Then you could have a stable and portable and free IPv6 address for life. (It's certainly possible in theory, just not built yet — similar to how LetsEncrypt was "certainly possible in theory, just not built yet" until it was built.)
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That being said, if you really want this to be DNS (not sure why; if it's not a short memorable name [and thus inherently competed over by typosquatters], then DNS is the wrong tool for the job), then you could do what systems like ngrok do, but directly serving those dynamic records as domains under its own gTLD, rather than serving them as subdomains under a domain. Maybe with each domain getting its own DNS zone and everything. That'd certainly be neat.
Note that way back when, the .me ccTLD sort of did this — they gave away .me "domains" for "free"; but with all web traffic on those "free" domains being intermediated by their L7 reverse-proxy servers, where they'd inject ads into any delivered HTML pages.