In a pre-print I read that "The position of the particle is indeterminate as it could be anywhere along the wave packet. Hence compressing the wave packet to reduce the indeterminacy in position will change the wavelength and therefore the momentum, and thus make the momentum indeterminate, and the converse", as an explanation for HUP.
Is this explanation accurate for HUP?
Well, the explanation is very qualitative but I think it works. What the explanation is trying to say is best conveyed by a picture:
As you can see, a broader wave packet in position space makes the corresponding packet narrower in momentum space. This is closely conected to a property of the Fourier transform (a very nice and easy to follow introduction of the Fourier transform, along with this particular property are discussed by 3Blue1Brown in this video and this other video).
You can also think of this argument in terms of the actual HUP $\Delta x \Delta p\geq\frac{\hbar}{2}$: if the distribution is narrow in $x$ then $\Delta x$ is small and thus $\Delta p$ must be large.