Soooo ... my own perspective on what's likely going on here, maybe it might jog SE to check into that instead:

I don't think it's the graphics drivers.
I don't think it's your hardware.
I don't think it's FFXIV per se.
Honestly, I think it's actually the launcher, combined with imperfect Internet connections, and XIV's notorious lack of any kind of client data integrity checks.

Personally, I've seen the DX errors on two occasions.

Once was during the latter weeks of Eureka: Pagos being current content, and if memory serves, the errors only happened in Pagos. It spontaneously went away when 4.45 dropped and Eureka: Pyros came out.

Once is currently. The game itself works perfectly, but I've been noticing DX errors if I click Exit Game.

Different PCs (the one I used during Eureka had nVidia, and the one I have now has AMD), and I know my current PC has been put through its hardware paces (I also play Chess extensively, including once generating a set of 6 piece Syzygy tablebases - which literally have to be bit-perfect, so it's extremely unlikely there can be any problems with the RAM or CPU, while just in case I've put the GPU through a torture test with FurMark without incident).

Now keep in mind that FFXIV verifies its client data integrity extremely poorly under normal circumstances, and a chronic issue seen by many players has been the "unable to complete version check" one during patches, as well (remember the heartbreak that was Shirogane launch due to so many people losing out right at the door because version check failed and they had to stop and reinstall the game, after which the houses were all gone - and then SE decided to pull the ultimate hold my beer by adding in the FC restriction and timer shenanigans with 4.2 so most of those that missed out on Shiro missed out on houses throughout Stormblood?).

My guess: People's FFXIV installations are slightly corrupted as a result of Internet blips (I don't think we need to list the weight of evidence that SE barely thinks about the state of the Internet in the West at all), and the failure of the game to check its data robustly, and that is what ultimately results in the DX errors.

It would handily explain the Eureka experience at least: Eureka was updated in 4.45 to account for Pyros, so presumably my Pagos related data from the previous patch was corrupted, then it got overwritten by a good copy from the update.