Take a look at Pokemon Rumble World. It's a new model they're calling "free-to-start" and Nintendo is claiming it's the model they'll follow for their mobile games.
Basically you get a full game with time limits, the limits become more restrictive the longer you play, but you can unlock those limits by paying.
In Rumble World, for example, you occasionally get gems and with these gems you can buy hot air balloons to take you to different regions. When you first start you have one region and basically can keep visiting it over and over, but as you go up in level you need to wait a minute or two before you can play it again, up to half an hour at higher levels. You can use the gems you find (or purchase with money) to buy more hot air balloons, each with its own timer; so you can visit one region, have a 30 minute cooldown, visit another region, then another, then another, and by the time you get back you've done them all there's only a couple minutes wait on the first region again. You've also been playing for about half an hour and that's a good place to take a break. If you don't want to wait you can use gems. Some of the later stages have one or two hour long cooldowns, but at no time are you completely unable to play.
This model gives you a huge boost to start, lets you actually play the game for an extended period of time when you install it and get a feel for whether you like it or not, and only need to spend money to buy gems if there's a very specific thing you want (like you REALLY want the balloon to go to some specific region but don't want to wait 5-10 days to collect enough gems).
The other aspect of the model is a hard limit on how much you can spend: in free-to-play, the more you play, the more you want to play, the more you need to pay to keep playing. With free-to-start, you start playing for free, you enjoy the game and want to play more, you pay some money to continue playing, eventually you hit the cap and you have now "paid" for that game in full and you get various bonuses unlocked, like no cooldowns on the balloons, a steady stream of gems to buy whatever you want, etc... If you like Rumble World it'll cost about $30 to unlock it entirely.
I am actually kind of intrigued by this model. Lots of games it can apply to. Think about a racing game, completely free to start playing, and you can unlock and race on all the tracks, but with cooldowns before you can rerace each track. Maybe you really like a specific track so you plunk down the 10 cents to play it again, and again, and again. Eventually you reach the limit and BAM no more cooldown, play it as much as you want, you've bought the game. Or you just like playing the different tracks casually for a half hour and it doesn't cost you anything.
Won't work for every game but there's definitely merit in exploring it, much better than the current "free game but it'll cost you $200 to unlock everything" model.