Why do so many textures look like they are from a ps2 game?

[Catwho]

I think its unlikely the developers responsible for textures are the same developers writing the story.

Definitely not the same team. It comes down to "resources" not time or bodies. Resources is software dev speak for "how do we spend our money most effectively?"

We already know they pretty much have a budget set by Square Enix, for which they can use to hire a certain number of people. They could hire another artist (or 3-4) who do nothing but make HQ resolutions/textures all day. Or... they could use that money for better data center engineers and equipment. Or more external affairs development (like the wedding stuff that just got announced. Etc.)

Early on they made the decision that HQ textures were not worth investing in. Maybe they will revisit that with more 4K televisions and monitors being used for this game.