Why is it that disk storage has increased exponentially over the years, while disk access times barely improved?
Why would you assume the two are related?  Think about it.  Disk capacity has increased because bits were shrunk and ever more fit in the same area.  All else being equal, the physical dimensions of the disk are the same with more bits crammed into the same size.

Traditional rotating disk are read by mechanically positioning the head over the right track.  The mechanism has to travel the same distance regardless of how dense the bits are.  In fact, the positioning accuracy needs to be better roughly with the square root of the capacity.  So the real question is why aren't newer disks slower to access.

There have been advances in the mechanics, how it is controlled, and how its position is detected, but those have a lot less room for enhancement.  You're not going to be able to make a mechanical gizmo that has to do about the same thing smaller, lighter, faster, and cheaper by a factor of 2 every 18 months just because the unrelated technology of transistor fabrication works that way.

There are really two access times for a normal rotating disk.  There is the track seek time and the latency to access the start of the sector.  The seek time is mechanical because it envolves moving the head.  The time to start of sector is a function of the rotation speed.  Newer disks do spin faster.  This not only reduces the sector wait time but also increases the data transfer rate once everything is positioned correctly.