Although what you're saying there is a logical extension of the concept of phantoms, that's not what the Wizard tv series really tried to do. Every phantom in the show was created by Fueki's ritual, and none at all were created afterwards, with that fact being explicitly stated in the series. It doesn't seem like the script writer realized that a gate wouldn't need a phantom haunting them in order to fall into despair...
Technically, from the perspective of the Phantoms in the series, their orders were to hunt down Gates and create more Phantoms from what we saw, right? And the end goal of Wiseman, from the perspective of Phantoms (I can't remember how much he was telling them when, but I'm pretty sure it was understood by them this was the goal), was to hold another ceremony that, as far as they knew, would lead to more Phantoms. It sounds like an aimless goal at first glance, but considering they're essentially a sentient species that's stuck in another species body until a trigger lets them out, it's an understandable motivation to have, I think.
What's more,
none of the Phantoms were actually "created" by the ritual - unless I've had a drastic misunderstanding of Wizard for a couple of years now, they were already
there from the beginning. What Fueki's ritual did was just bring them to the surface. We know Phantoms "inside" people are sentient creatures by looking at Dragon, and we can't forget that Chimera is proof of Phantoms before Fueki as well. It definitely is a poor showing of the show that we never had a Phantoms born from Gates just falling into despair normally, but Phantoms themselves were never described as something Fueki actually created, just something he influenced with his ritual. If they were, the whole concept of Gates (and in turn most of the show) wouldn't make sense, because he had nothing to do with those people beforehand. They just were unlucky and were born with Phantoms in them.
Obviously the show didn't take advantage of... pretty much all of these things (it's one of my biggest issues with anything in the franchise, just how much Wizard could have done with what it offered but didn't), I'm not denying it at all, but they
were all elements presented at points, if nothing else.