Cursive writing and recognition was taught because it was how adults communicated with one another quickly... in the past. Modern day adults (and most teenagers) use computers for quick communication, and there are less and less usages for cursive writing. Personally I can't remember the last time I had to write anything long by hand.
Efficient typing skills, on the other hand, is absolutely essential for day-to-day life. It will also probably only increase in importance compared to writing cursive. I meet far too many adults in the work force who still can't type properly, and it drives me absolutely insane that they don't have the basic skills necessary. This is not to say to not teach how to write print form, otherwise known as block letters. Children should of course know how to write with pen and paper, just not specifically cursive form.
Also, keep in mind that arguments like "well most teenagers know how to type" doesn't relate to curriculum. First and Second grade teaches things that seem like perfectly common knowledge, such as "how to tell time", "identify shapes", and "recognize and write numbers up to 100". It's not about what you as an adult would like to learn, but rather what should be part of a core skill taught.
Edit: of course if there is resource to teach both then they should teach both, but this is under the hypothetical that there isn't extra resources and time for it. We could talk about reforming public education systems as well.
Edit 2: apparently I misunderstood the dedinition of touch type-- thanks for pointing it out.