So like, it's basically there to encourage you to come back later because the game always leaves you waiting for more.
Really all it was to me was annoying. I used to play these games, and the moment I had spent money on better games that didn't do this, I stopped touching Zynga products and moved on. I get the feeling that isn't what they were going for. I kind of prefer to define my own times to play games, you know? I really don't like when the game declares that my session is over, or when the game says "You can't play for x time because building is under construction." I never exactly dove into arcade games either, for that very reason.
Yet, there is a game where I DO like the energy system. Spiral Knights lets you buy energy with in-game currency. If you're good enough to make enough money, then you can actually buy back more energy to play more levels or wait for energy to recharge. I really prefer the systems where the players can exchange in-game money for something that you'd normally buy with real money. Partly, I mean, it doesn't really hurt the company too badly because someone has to buy that in the first place. Someone else bought the energy that you were looking to buy. It gets into the economy and leaves the economy in such a way that someone out there is spending money on it and letting the players who play the game for real actually play it for real more often. And yet, in Spiral Knights, you can't spend your way to success because buying anything remotely advanced requires a lot of farmable materials... and then you need to level up your gear by using it in levels. So, early players can't shortcut to the endgame by buying tons of energy to buy in-game cash.