I mean sure nature has no obligation to not have a unfalsifable particle, but you wind up in weird places, like, there exists a distribution of dark matter that explains the poltergeist that knocked over your coffee cup last week.
We can measure the mass distribution on astronomical scales. We "see" the dark matter. Just not with light.
It's not crazy different from saying the same about that poltergeist.
We know of particles which behave the same way. Neutrinos for example.
We are not measuring dark matter, we are measuring something that is not what we expect and we decided it's dark matter.
You act like we've managed to probe the depths of physics with certainty when in reality you find any means to reject that which offends your sensibilities.
At the root of science is "sensibilities", like occam's razor, even "what counts as experimental reproduction", etc.