You begin a consistent trend here, which is making comparisons that are not equal. Releasing what is essential a Siege mode dungeon has a far different experience than anything the game currently offers. In that context, the mobs come to you and you're forced to defend against possible waves or do other objectives. Eureka is not this nor does it remotely compare. No matter how you approach it, you simply kill hundreds of mobs endlessly. It does nothing different. Saying the challenge log gives a different vibe is, again, subjective, and a bit silly. It's literally "kill 30-60 of this elemental type". That isn't variety, it's simply masking the same activity behind something else. If you simply try to spawn a NM, you'll inevitably complete the challenge log without even noticing.
In Anemos, yes. You can solo some NMs with a low enough instances. This isn't the case in Pagos. Regardless, the grind is so immense, you'll be there for ages. Will this be nerfed come 5.0? Yes. But previous relic steps didn't require a nerf bat for players to catch up. That is the complaint many people have. If you're starting the relic late, it's an increase grind right now and you either deal with it or wait until the expansion's conclusion to maybe have a sensible alternative. There is no way around that being poorly thought out.
Lots of "ifs." This assumes only a small portion of the players did relics. Lets put that aside though. If we assume Eureka and the relic were always intended for a niche audience—a Savage equivalent or thereabouts. What content is there for the general audience; the overwhelming majority? Unless you like virtually every activity this game offers, you'll be finished in under a month. Eureka can't be considered niche content because there just isn't enough for the general playerbase to do otherwise.
You missed my point. Put the relic in Diadem, even with randomization akin to what Pyros has now, and I guarantee it doesn't die within the first week. Put simply, the relic is what keeps Eureka somewhat populated. Any other weapon set and I suspect those population numbers dwindle even if said weapons were guaranteed; no random rewards. I hardly think people will care about say... the i380 Armor sets they threw in there.
A silly "question" yet one you built a Strawman around. First and foremost, I said nothing about tomestones and used light grinding as an example. Regardless, every single example you provided has no need for a tomestone solution because there either isn't an arduous grind behind it or it already has a solution to remedy said grind. 10 EX Primal tokens guarantees you a weapon and the mount can be obtained with 99 should you elect not to grind further. The drop rate also increases significantly in subsequent patches. Savage has books to combat its RNG aspect, but also rewards the best gear currently obtainable. The minion/mount are guaranteed drops that simply require a re-clear to obtain. And even if you were unlucky enough to lose in every single pug clear you do, Savage eventually gets unlocked, making it possible to farm everything.
Everything has an alternative here... except Eureka. So this tomestone example falls apart before we even touch the Achilles' heel. Both the Zodaic and Anima relics had an alternative method of progression; multiple, in fact. You keep trying to pile on things like the challenge as some unique deviation when it literally revolves around the same premise—so much so you'll often complete it while spawning NMs because killing trash mobs is the only option in Eureka. Allowing people to tomestone or light farm outside Eureka is simply bringing back the previous options taken away.
As for your tomestone calculations. People have already pointed out they are absurd. Since we already know Pagos requires 500 tokens, 50 Mendacity—a third of what you suggested—necessitates 25,000 tomes, which roughly puts it in line with the Umbrite step. Now you have options! People who abhor tomestone grinds, like yourself, can happily farm NMs while people who prefer it or are indifferent can do dungeons, trials or whatever. This is the crux of almost every complaint: a lack of options. Eureka forces a specific style of gameplay onto people with no deviation. Change that and the complaints will die down.