We limit screentime because it's bad for the eyes and we want to encourage physical activity. EnviroKid did not watch any TV or computer until he was 2 because that's the AAP recommendation. After that we began letting him watch some things with close supervision. Just before he turned 3, he learned how to use the mouse and we began letting him play some computer games for young children.
My father got one of the first home computers (the original Apple II) when I was 4 and my brother was barely 2. He began letting us use the computer right away, for short periods of time with supervision. He also began right away explaining to me how the computer thinks by following a program. He wanted to write a program that would do mad libs (it asks you questions and uses your answers in a story) and I sat with him helping to decide the details and watching how each answer from the user was encoded in a variable and the computer then plugged in those answers in place of the variables in the story.
This was extremely educational, and not just for the purposes of learning computer programming. One of the few battery-operated toys I ever had was a Speak & Spell (it tells you a word to spell, you type in the letters, and it tells you if you're right or need to try again) and after a few minutes of playing with it at age 6, I realized it was just running a program with variables, and I got all excited and tried to write out the program (but gave up because it was so long and detailed). Same thing when I first saw an ATM at about the same age. As computers have proliferated in our everyday life, I've always been aware of the basic way they work, and that makes it a lot easier for me to get along with them and not feel intimidated.
When I was 8, my dad tested the database software he'd written by helping me create a database of my stuffed animals. This required much more thinking on my part than the computer's! I had to decide what the fields of the database should be, which should be text and which should be codes, and what categories to set up in the coded ones. Thus I learned the difference between a string variable and a categorical variable, and the limitations of each--which was really useful a decade later when I got a job setting up an address database.
I could have learned these things at a later age, but IMO starting early made them easier to pick up and more natural-feeling. I did NOT become someone who neglects non-computer skills because the computer is easier--I have lovely handwriting and prefer to do arithmetic by hand!
I'm now the data manager for a research study, so I use computers all day long, do some programming (consolidating data with algebraic algorithms, and running statistical tests), and often set up databases that are not much different from my stuffed-animal one.

I have to learn new stuff all the time, but I still think that my early foundation is very helpful. I've been at this job almost 11 years and have trained a bunch of people, and I've found that those who have a background in computer programming but not statistics actually catch on better than those who have a background in stats but not programming.
One of my CS-major friends in college said, "I don't understand how people who can't code can THINK." I wouldn't go that far, but I think that a basic (pun intended

; BASIC is still the best language to start with!) knowledge of programming helps people learn to organize their own thoughts and operate more logically. Not that logic is the most important thing in life--intuition is very important too--but it's certainly useful! I think programming also improves people's ability to "get with the program" i.e. to figure out how a process is operating even when it's outside the computer, for example the steps in making a certain kind of sandwich. (I noticed this working for Dining Service at a university with both CS and fine arts students.) Of course it's also important to think critically about the program rather than following it blindly, but being quick to see what the program IS is handy there.
Anyway, I agree that computers are of pretty limited usefulness to preschoolers, particularly compared to other things they could be doing, and when they do use them it should be mostly with adult interaction as well. However, I think computer literacy is important in the concrete operational period (about 7-11 years old on average) because that's when kids' brains are really primed to pick it up. It appears to be harder to learn totally new computer skills after about age 12, just as it's harder to learn to speak a new language really fluently after that point.