Your v6 subnet prefix is no different than whatever WAN-side v4 your NAT had. "Accidental semi-randomization" of the WAN side IP is not something one could reliably count on. Many ISPs just hand over a static-like IP, that is, even when it's supposed to be random the pool of IPs is so constrained that it's usually the same simply through the IP lease surviving power cycling. And that was before CGNAT.
If your concern is being identifiable through your IP then counting on whatever v4 artifact is the wrong move. Use a VPN with randomised exit nodes.
It’s of some practical real world value that people cannot resolve v4 IPs to individual households with certainty. It’s a shame to lose that value.
It’s very unclear to me why people should be able to deterministic reach out to a specific device on my network. It has no value to me unless I run a service.
Also... the ability for people to deterministically reach out to a specific device on your network is the exact same ability you use to deterministically reach out to specific devices on their networks, just viewed from the opposite side. If the Internet wasn't a place where people could decide to run services on their networks and connect to services that other people ran on their networks, what would the point even be?
IPv6 supports customer-controlled prefix rotation. You can select how often it happens by configuring your router to periodically change its DUID. Of course, your ISP can ignore this signal and always assign the same prefix anyway, but you can hardly blame that on IPv6.
One of the biggest changes from IPv4 when I enabled IPv6 a while back was that it’s fine and normal to have multiple addresses per interface now. ULAs are not globally routable, so I think of them as LAN addresses. Another option that comes to mind is mDNS, but I think support for that is not as widely accepted.
Global addresses can change, just as your home dynamic IPv4 probably did from time to time.