They can't pass up the promise of being taught a spell they'd never be able to learn otherwise due to their shorter lifetimes. Even though Frieren disrespects her constantly, humans treat Serie as a godess because of that.
We also learn its only be 50 years since Serie finally passed someone to first class...pretty sure that conflicts with previous lore directly, but nobody seems to care that this series can't keep its lore straight but me.
I will never defend this arc. I personally think it is shit. Completely out of tune with the rest of the series that is fundamentally better. It's loaded with bad writing, contradictory lore, plot contrivances to close plot holes, etc. I dared to criticize it and got moderated on another forum for it, haha.
I seem to remember manga readers not being particular fond of the magic exam arc either for much of the same reasons, but once it is animated all pretty it is a sacred cow.
What we can assume is that the old guy probably fights the examinees one-on-one and kills half of them, because the Magic Association are elitist assholes who think they know better about magic than anyone, and they're blindly following Serie's philosophy that magic is primarily for war.
The pendant Frieren has also shows her that Serie isn't a final authority, just the current one. Her pendant from the Church was the equivalent or greater achievement than getting First Class certified in present day.
Serie does this because she's looking for another Flamme. She just found one in Fern. She talked a lot of shit to Fern, but she still wants to satisfy her first student's dying wish. It's all the more irritating to her that her hopes in Flamme's promise are tied to Serie's philosophical opposition concerning magic. Serie she has too much pride to fail Fern arbitrarily because she would remember for the remainder of her days that she squandered someone who she actually holds interested in over a petty grudge.
Methode is one of the bigger reasons I hate this arc, especially the 2nd test. She possesses a wide array of abilities strictly for plot reasons because if she didn't, the bad writing would be full of holes in how the 2nd test is conducted.
edit:
- No healer because this is mage exam? She has a holy book and is quite good at healing. (Frieren also has one)
- Probably the most dangerous clone is Fern after Frieren and Sense? Methode has exceptional mana sense!
- Not sure where all the clones are and worried about an ambush? Methode's mana sense goes far! (So does Denken's)
- What if we need to restrain Fern's clone? Well, Methode specializes in that as well (but didn't she specialize in shield magic an episode ago?)
The author also forgets when they previously established users who can do similar stuff but for some reason don't during this exam?