I think the Horn of the Goblin General is based not on the loyalty but on the status of the person using it. In the anime, when Enri first used it it summoned about 25 goblins but after she became Chief she was able to summon the 5 thousand. There will be some who disagree but then why would the story need to include a part of her being chief? The only other point that Enri being chief was necessary was when she asked everyone whether they wanted to stand with or go against the 5k army. Or it could be the condition that they are fighting 5k because players don't fight that much monsters in caves at once and even if they do their first intuition wouldn't be "ok I'm going to summon some a few goblins to help me