1) So are we going to say that level 3 sheep in La Noscea are designed for ARR and HW Relics because "You need the exp"?
Also, the Relic itself doesn't actually need the experience, you only need the experience to progress through the story which unlocks Gerolt.
2) So are all ARR FATEs and HW FATEs designed for their Relics too?
3+4+8) So you're telling me that you can do FATEs and have a chance to get an item that is necessary to progress your Relic?
I wonder if I've seen that mechanic exist in this game before...
6+7) Light farming. Brand new mechanic guys. Never been used before in the entire game and can never work outside Eureka. /s
9) Wow, you can do a Specific Dungeon and get items for your Relic! Wow, colour me impressed, I'd never thought I'd see the day when that was the case!
Also note: You can buy Logos off the MB.
As I said before, exclusively locking progression behind the content doesn't make the content "Designed around the Relic". Since it's literally the same as arguing that any of the content that was usable with previous Relics was "Designed around the Relic".
Especially given that the things that Eureka gets you to do, are almost exactly the same as with previous Relics, only instead of being done in the natural Overworld or via Duties accessed via DF, it's done exclusively within Eureka.
An example of a reward being designed around some content would be the PotD/HoH rewards. Where you go into the Unique Content and utilize a Unique Mechanic within that content (Finding Silver Chests to level up your gear) in order to earn the reward. Or another example is with difficulty of content being designed around, such as how the Savage item level gear comes from the Savage content which is uniquely more challenging than the normal variant.
Just putting in half the effort just to limit the ability to access something to a specific piece of content as opposed to any other similar content (Such as Overworld FATEs or DF Duties) isn't designing around that piece of content.