During the big "10 Years" LL they did after Endwalker, they mentioned the final Named Ascians that they have true names and that they have their backgrounds, should they decide to use them in the story in some way.

Here's the post with the translation, and here's the Q and A:

Q: Are there sundered Ascians (other than Fandaniel) or black-masked Ascians of lower ranks still around? I’d also like to know which Ascians those two red masks that Gaius carries around belonged to.

A: Perhaps a few of the sundered Ascians are still around, though it’s unclear whether they would be on the Source or one of the Reflections.

The masks Gaius carries around once belonged to Altima and Deudalaphon. However, Gaius simply had their masks, and whether or not he truly vanquished them has yet to be clarified. A point you may want to consider in your theories is what it takes to vanquish an Ascian.

And

Q: Will we have a chance to learn the identities of the full Convocation of Fourteen?

A: Their true names are already decided, but whether they’ll be revealed or not depends on how the plot develops in the future.
Despite there being some "okay no more Ascians" I do think tying up those loose ends for good would be a good idea so they're not just... there. I would think that the WoL and the Scions would know "we only dealt with these, so there are at least a few more out there." and... you know... want to deal with them. They aren't like their Unsundered counterparts, sure, but the threat of them there trying to stir up trouble wouldn't be there if they were dealt with.