I’m using my scroll wheel on my Kensington Turbo Mouse right now. It works just fine, as far as I’m concerned. Plus, the way the scroll wheel on the KTM is configured, I use my middle finger and thumb alternately to scroll, instead of just a single finger on a conventional mouse scroll wheel, so it’s faster for me (I’m fairly ambidextrous with mouse inputs, and use a conventional mouse with my non-dominant hand-- old practice from my sysadmin / tech support days, being left-handed and having to use others’ right-handed mice when I would troubleshoot their computer issues. So I am live-comparing the two).
I’m perfectly comfortable using a trackball, although it wouldn’t be my first choice, which is a Magic Trackpad. Mice are 2nd-best.
But, the one pointing device I can’t stand is a pen. I have an artist friend who uses a Wacom tablet for everything. I can see where the pen might be important for drawing, but using it for all the other computer operations just seems painful to me. Makes me crazy when I need to work on her computer.
Me, too, for the reason that, when I have to sign a scanner for a credit charge, my signature looks horrible. I wouldn’t pass a sobriety test with the awful scrawl that passes for my name. LOL
I’ve exclusively used a Logitech thumb trackball for many years. Started with wired, now wireless. I actually have two of them - one at home and one kept in my suitcase for travel.
Hadn’t thought of it before, but I can’t remember the last time I touched a traditional computer mouse.
Here is a truly enlightened human being! 
All I really see is you holding a ball. - Track Ball. 
“Computer, set course for Alpha Centauri, Warp 7”
Hah! How big would the device have to be in order to house a ball that big? LOL
I use a wireless sideways mouse from Logitech (they call it “vertical” but I think sideways is more accurate) to reduce wrist stress. So it leads me to wonder how a trackball compares to an ergonomic mouse for repetitive stress? How much of the time is your arm resting on the desk, when using a trackball, vs. being above the desk and supported by the shoulder? And when your arm is resting on the desk, is your wrist still doing most of the work (as with a mouse)?
I’d like to like them, but any flavor of trackball gives my hand pain in short order. And I know this because I started my career as a hands-on helpdesk tech and would have to use them on user computers that had them installed.
Oooh, I’m so sorry! We don’t want that but, because of our special “injury clause”, you are still an honorary member of the “Trackball Club” anyway. LOL
For what it’s worth, you are correct. A mouse is definitely an upside down trackball. The trackball came first, by about a decade or so (IIRC).
I’m also on team Trackball. I’ve been using a logi trackball, purchased out my own pocket, at work since 2011. Not needing desk real-estate is a huge thing for me and I simply prefer the feel as well. Mine is a wireless so when I’m doing presentations I can even using it while standing up near the screen, and holding it in my hand, so that I’m not chained to a location in the room or constantly saying “next slide please”.
What?! I don’t remember seeing one as a kid. What happened to it?
I’m trackball all the way. I still use one of these. it’s easily old enough to drink.
The first mice used two wheels at right angles to each other. Various non-mechanical means were developed using a special pad with a grid of embedded wires, using capacitive coupling to detect the position on the grid I believe.
Track balls and rollerball mice developed in correspondence. They were a return to the two wheel system, only the wheels rolled on the ball instead of a flat surface. The track balls were dominant at first with no concern over additional space and the proper rolling surface.
Optical mice on a special pad with a grid of colored reflective lines became popular for a while as the cost was initially much lower than a mechanical device. As the mouse market grew the roller ball type became very popular again, before newer optical mice that worked on most available surfaces became dominant. Several factors contributed to that including wireless connections and sensors that required very little power and could last for a satisfactory time on a single replaceable battery.
Of course a trackball is just an upside down roller ball mouse with the buttons inconveniently located.
I’ve used a trackball for many years. Lots of upsides, like you can relax your tracking arm completely instead of having to keep some tension in it most of the time. Also, per the quoted statement, my cat can rest her head on the back of my perfectly stationary hand while I work and she naps. Also, you don’t need any particular surface to put it on-- you can put the trackball on your thigh if you want to. Also, because it’s still, it doesn’t pick up dust, fragments, or (ahem) cat hair from the surface it’s resting on. Frankly, I can’t think of any good reason to use a mouse.
I use this Logitech Wireless Trackball.
An intelligent and discriminating user! 
I have a coworker who exclusively uses a trackball and watching her manipulate it stresses me out. It seems way less accurate than a good ol’ mouse. Definitely slower.
Maybe she’s just bad at trackballs, I dunno. For me it’s an ain’t broke/don’t fix situation.
Trust me, it’s her. No way would sliding a mouse all over your desk be faster than rolling a ball with your thumb or middle finger.