> That still requires trust stores to be distributed to the clients
There's no such thing as a "trust store" in practice. To be "trusted" you just need to demonstrate you have control over a DNS TXT record, and we don't need a special "store" or intermediary for that.
Certificate authorities are an artifact of a bygone time and an entirely different model of internet infrastructure.
The trust store refers to the collection of parties that ultimately verify the signed claim of your control over a domain, which might have taken the form of a DNS TXT challenge (or any other number of challenges). You still need it, because there would otherwise be a basic circularity when determining whether to trust a connection.
(Moving the PKI into DNS does not remove it, it just moves it around.)