Which (if any) public TLDs permit for such subdomain configuration?
They all should. However some registrars may prevent it due to restrictions in their web UIs. You should consider this a bug and complain. It would be useful if you reported any registrars you find doing this.
How many DNS requests, pertaining to the domain, will be served by IPv6-only servers?
Most DNS servers that are configured for IPv6, filter out any AAAA records if the request came from IPv4. This is done as a precaution so that misconfigured IPv4-only hosts don't try to connect via AAAA. In other words, if a host is able to reach the DNS server via IPv6, then it is safe to tell the user to connect via IPv6 too. Sites like Google did this when they enabled IPv6; I'm not sure if they've stopped doing it since "World IPv6 Day".
How accessible (from the Internet) will the domain be if all IPv4 NSes went offline but IPv6-only ones continued?
I don't know. In theory, some DNS servers may be doing their queries under IPv6, but most likely very few. However I can suggest a test that would help you predict the answer.
If I was going to make a change like this, first I would set up an experiment to test the above hypothesis. For example, set up 2 NS records each with one A record and one AAAA record. Run in this configuration for a week, keeping logs of the requests you get. Calculate what % of IPv6 traffic you get. Calculate what % of queries were received via IPv6 but produced answers that did not include AAAA records.
I would do this test no matter what. There are too many ambiguities in how ISPs configure their DNS servers.