I do all of those things and code something of interest to me and my company has no 20% time. I understand, you'd like more time to do those things, but time when we get to do whatever we want is called a day off.
Look, if you want to study web frameworks, tell your employer you want to work 4 days a week and spend a day studying for yourself.
How's the conversation going to go?
"Can I spend every Friday learning this new web framework? No, we don't use it, but I think you should be supporting me increasing my skill set. Yes I still expect to be paid."
