If it was concentrated in only specific spots it would cause different gravitational effects such as lenseing.
The lack of lenseing isn't the only issue it's also the general mass distribution across the galaxy for example the stars in the outer parts of the Milky Way move at nearly the same speed as the stars in the center. Since the center has much more mass the stars should move faster but they don't which means there is a lot of more mass that we do not see and that is distributed evenly across our own galaxy and not clustered in the center like the normal matter.
So to match the observation the dark matter has to be every where think of it like the air around you.
Now it doesn't have to be actual dark matter but it has to gravitationally affect the rest of the matter in the universe one of the version of string theory has dark matter as gravity leaking into our universe from higher dimensions or parallel universes the problem with that is that it still does not explain the diffusion unless the brain it's leaking from for some reason unlike our universe is diffused.
https://en.wikipedia.org/wiki/Gravitational_microlensing
You're right that all the dark matter in a galaxy would contribute to gravitational lensing around that galaxy, but that's a different signal; you'd be looking for the lensing at different scale, e.g. Einstein Rings around the edge of the galaxy, not inside it.
I meant 'diffuse' literally, in the physical sense, as in sparse, not dense -- the 'missing mass' that we're trying to explain is, under the dark matter hypothesis, spread out more thinly than if it was accounted for by dense dark objects like planets or stars.
So what do you mean by diffuse and could you point me to some source I can read up on this?