Sorry, but not all can become stronger through experience and not all can become what it is necessary for becoming a first class mage. That's why there are called rejects, not enough for the task, these first mages has the task to assist people through monster infested environment and any mistake could be fatal, so only the best can enter, plus failing doesn't necessary mean death, remember they can only pass if they captured the bird until the time set runs out. Those mages that died are too inexperience or unlucky to fall for a trap of a monster, that's on them thinking they could pass the test. Nothing said on the test that you will survive or they hands are being hold, those who just simply failed and not died could re enter the test in the future after they get more experience and get stronger as you said. They just died, nothing to talk about this any further, nothing to add, they are simply unlucky/stupid/weak and therefore died, its like those people who tries to become some elite soldier only to die in the progress of it, nothing against them it is just unfortunate.
yo there is a related manga that is in the web page right ? it is his work and his work is one of the best in the romance genre and to top it all his work is in a single universe it's like we just need an avenger version of his work here
well if you still somhow can't find it suzuka kimi to iru machi fuuka hitman
But it's clearly a fake anyway, not the life booster. That is why the original controller of it was thinking about how to not give it up so easy that it's suspicious. He doesn't want it because it's fake. Instead maybe he has the real one on his person, sneaking off with it while everyone fights over the fake. Or maybe he doesn't even have the real one, and has other motives for them fighting, or knows where the real one is and goes after it while they fight. Anyway, it's fake.