I think that this problem will grow more and more within our profession.
The era of code-monkeys is over. Today software development has not been easier. We have a huge amount of productive tools out there to make our day to day work much easier.
Developers, or programmers (architects, technical-lead, senior ..., gurus or Computer Surgeons) should be innovative and up to date with the latest technology. To be that, one must explore and learn new things constantly. For a short period in most peoples life, that can be done during evenings and late nights, but sooner or later you will neen all your spare time for other duties,
The very often quoted 10:1 myth regarding developer productivity clearly states that there is a hidden capacity reserve among everyone working with software development.
So if a 25% increase in productivity could be achieved (1:10 is 1000% between low and high), that increase would easily compensate for the 20% time lost by spending time on pet-projects or other stimulating and encouraging activities.
What I mean is that the Google 20% is not just a nice thing to brag about, it's more than that, it is a true recognition that the most creative and innovative employees require that. Even in workplaces where 20% time is not provided, people still spend 20% or more time doing stuff not work to real work.
It's the oldest trick in the book, even Leisure Suit Larry had a "Boss key", the Boss key today is called Alt-Tab, or write your SO answer in Emacs inside a javadoc comment and paste it in during a calm moment (if you happen to work in a real coding slave dungeon where you are constantly being watched).
So try to convince your employer that they allow you to spend 20% of your time on whatever you want (related to your profession as a software developer), as long as the other 80% keep you focused on doing what's expected of you to earn your pay check.