While we don't spend all our time in front of a computer typing, it does seem to represent a non negligible portion of our days. Assuming an hour a day of typing on average for the rest of your life, the time you will spend typing is tens of thousands of hours.
I'm currently learning Dvorak and it looks like it's going to take about 30-40 hours to be able to type properly. So the gains in efficiency don't have to be very significant to pay off.
To check how efficient the time investment is I checked my typing speed. Like you, probably, I'm not a touch typer but I felt like I was typing pretty decently before, and measured at 40 wpm on both of the two websites that I tried, with no mistakes. I'll check my speeds with Dvorak once I'm done with the lessons, and again after a few months of practice, to settle this debate hopefully, but just from having done the first ten or so lessons I can already see that Dvorak is going to be a major improvement, if not in speed, definitely in terms of comfort.
You make an interesting point about likely spending over 10k hours typing over the course of the rest of our respective lives, although I note that even if you are right, I'd have to invest 30-40 hours now in order to learn to touch-type, whereas the gains would be spread out over a longer period. That said, please post your results when you get them, I am definitely interested in hearing about it.
I do note that you conflate two distinct issues: whether touch-typing is worth learning, and whether Dvorak is a meaningful (or any) improvement over QWERTY. I am definitely far more suspicious of the latter claim than the former (see my link in the grandparent for a thorough debunking).
Thus spake Eliezer:
It seems that many here might have outlandish ideas for ways of improving our lives. For instance, a recent post advocated installing really bright lights as a way to boost alertness and productivity. We should not adopt such hacks into our dogma until we're pretty sure they work; however, one way of knowing whether a crazy idea works is to try implementing it, and you may have more ideas than you're planning to implement.
So: please post all such lifehack ideas! Even if you haven't tried them, even if they seem unlikely to work. Post them separately, unless some other way would be more appropriate. If you've tried some idea and it hasn't worked, it would be useful to post that too.