"John, you make it sound easy, but who knows how big this world really is? If we don't find them, it's a real waste of time."
"So for now, let's focus on hunting dragons. If we encounter S.'s team, we'll stick to them! If we're unlucky and don't find them, we'll just do our best."
The reason for the explosive increase in S.'s team's hunting points is simply because most players haven't noticed this loophole in the rules and thus haven't been too cautious.
Once players realize that their hunting points are increasing suspiciously fast, they'll naturally become more vigilant.
Unfortunately, after John switched to the Alchemist class, one of his biggest regrets was losing the unique thief class skill [Blood Trail] that allowed for long-distance enemy tracking.
This was something even alchemy couldn't make up for.
Although the bird could also track targets by their scent, there were some unavoidable usage limitations.