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It does. Here is someone who lists all of the .horse domains just in case you would want such a thing [0]

Why wouldn't it?

Because different tlds are operated somewhat differently and afaict this seems to be a secondary service that isn’t fundamental to routing or other required operations of a registrar.

In this case it seems to work with “participating tlds”, whichever those are.

All DNS zones on CZDS have the same format, and AFAIK all nTLDs are required to use it.

But you're right for ccTLDs -- everyone uses their own format and most don't even allow you to get the zone file. There are some companies though that provide similar lists from crawling data (e.g. https://zonefiles.io/).

yes, but you need to request it