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Yeah, but you can have that only at the edges, using ipv4-to-ipv6 proxies to connect to the Internet.

Yep; this is what T-Mobile already does if you set your phone's APN to "IPv6 only".

Similarly, my cable modem (which is distinct from my router) only gets an IPv6 address from Comcast.

That's only a management interface tho, the modem will still happily forward ipv4.