Why did trackballs disappear?
To start with, they didn't. They are still around and can be bought in many variations. For example, Kensington sells six kinds of trackball, and Logitech sells three.
Only their time attempting to work as a general pointing device is gone.
Nub. Low-tech, cheap, compact and reliable, but miserably imprecise. Did they ever fix that? Is it even theoretically fixable or is it a limit on the precision of the human finger?
The Nub itself isn't imprecise at all. At a basic level, it's a joystick with no sense for urgency (speed), so various driver profiles have been developed offering non-linear movement - this in turn is something not everyone can get along with - especially not at first.
Touchscreen. Looks great when an actor is using it for ten seconds in a movie, kills your shoulder when you try to do it all day in real life.
In fact, I really like it. Back in my Newton days I was constantly hitting the CRT to acknowledge some message box - until I spent a lot of money on an early touchscreen.
Touchpad. It took a while to get the technology to work properly and even then it's awkward to use and takes up a lot of keyboard space. Modern laptops seem to have settled on it anyway, perhaps because it's thin?
In part, but also because it's more natural (see below).
Trackball. Fast, precise, easy to use, not even expensive.
If it's supposed to be fast and precise, it's anything but inexpensive.
Seems to me the trackball is the best option.
If you can handle it, then yes. For most people it doesn't work. At least not from the start. Computers have been optimized (or evolved) to provide a satisfying first-time user experience over an efficient long-time usage. Basically the same process that (almost) eliminated the keyboard as #1 interactive tool, despite being in most situations faster and more exact than any pointing device.
It's all about the learning curve.
Humans pointing somewhere don't use their fingertip to waggle around, but the whole arm and hand, while the index finger is just, well, the tip. That's the way we are trained to do since being a toddler.
Reducing this to just forearm and hand, with the finger giving the affirmation is as well trained into our Motor Cortex. That's why most people get along with a mouse without much training. It also adds that the mouse is 'glued' to the hand, so no active control for repositioning needed.
A touchpad comes next, as it's still pointing with the finger, but a restriction of movement needs to be learned, as well as a way to handle repositioning, as there is no haptic feedback for this.
Even the Nub comes before the trackball, as it works by applying force in the direction one wants to move the cursor. As intuitive as a joystick, just a bit more delicate.
While the trackball is an awesome device, once learned to use it, the learning curve is way steeper than with any of the others, as its handling goes against our natural movement.
So from a motoric point of view of an untrained person (beginner) the trackball comes last. This may be quite different, once time has been invested to learn to handle a trackball on an intuitive level. But that's not how everyday interfaces have been optimized. So track balls are, nowadays, back in the realm of experienced professionals.