I'm 28 and since I was 20 I have been saying there is never enough time! I'm an electrical engineer, I also write software for everything from PLC's, microcontrollers through to applications for Windows and linux (and if I feel the need on mobile platforms) I am currently in China for the next 2 months, working 75+ hours a week... There is no time... Saying that I still seem to be able to dabble in learning new things and keeping up to date on the things I already do. In my twenties so far I have studied and worked a hell of a lot, I didn't do it wrong as I have enjoyed myself all the way. I am one of few people who can say they love their job and I am extremely happy with my life. While I have no time, I still seem to make time for the things I find important. That is learning and playing with new systems. If someone doesn't find that interesting they would be wasting their time by doing it. If you are happy with how you work, what you know and the tools you use, awesome! Don't let other people tell you that you are behind the times or computer illiterate because you don't use their system or even understand it. But please don't be one of those people who hate the tools they use or the life they lead and don't make the effort to change and learn.
You took that idea to the logical extreme, dude. Nobody is saying that if you have even a little free time, you should be a polymath. But if you don't have time to learn a little something new (especially something that relates to the career field you plan to spend the rest of your life in), you either find the time, or you'll find your career stagnating before you know it.
Also, stop being offended by every comment that doesn't agree with yours. fit2rule's comment could be considered a bit presuming, but it is neither nonsensical nor condescending. On the other hand, your comment is both of those things.
Funny, I find that I like having a bit of time here and there to think -- not running around "being social," not spending time on assigned work. I wind up doing those three things better after some time to sort things out in my head.
Of course, I could be doing things wrong. Who wouldn't want to have every waking hour consumed by other people?