I have not played Triple Town but free to play model that generates revenue by asking users to pay for unlocking things is here to stay.
One clear example is, League of Legends. Where you start with set of free champions and you either play or pay to unlock more of them. One can argue that, Valve's TF2 and Dota2 are in similar vein. You of course, don't have to pay to unlock heroes - but you pay to buy cosmetic items (so as you can look cool in-game). So, while you may dislike this model, it looks like it is here to stay.
I also haven't played Triple Town, but I want to note there are multiple ways to go about free to play. I love the model Valve does with TF2. A player will be able to unlock a large amount of weapons through achievements and drops without spending any money. People may argue about balance, but there are no weapons which 100% outshine each other. Being a paying user doesn't really affect how well you'll do in game. Dota2 takes this further and you only pay for cosmetic items, with your character's ability having absolutely no correlation with how much you've spent on the game.
LoL takes a different approach: You can spend money to unlock characters. However you steadily earn money from matches. I'd call this a middle ground.
Most social and free to play games on phones and facebook take in my opinion the worst path: Paying directly and dramatically influences your ability in the game. I dislike this approach for a variety of reasons. The biggest is the ways it influences other design choices. I'd love to have a little game revolving around growing a good farm or city on my phone, but all the games I know about take the social approach. This means I have to go and wait around for something to build unless I pay, instead of having fun playing a little game. Imagine if tamagachi used the pay to win approach? That rich kid in the playground would've had an awesome pet, and everyone else would be left with a starving pet.
I agree, I have tried a few games with the wait or pay to advance dynamic. I much prefer to be able to progress as much as I want when playing, limited by the time I have to play rather than when the game wants to halt my progress.
The other issue is that it seems like often paying wouldn't be much fun either as it makes the game to easy.
I don't think the argument above has to do with the model of "unlocking things". The difference in League of Legends (and DotA2/TF2) versus most other contemporary (especially mobile) F2P models is that most of what you buy (your example being Champions) are permanent unlocks. I haven't heard a lot of arguments against that model. You're paying for a digital version of something that you now own, you keep, you collect, and you can essentially use forever. To me that's very different than buying something consumable (e.g. coins) or energy based that is literally spent and then gone, at which point you're expected to pay more.
More importantly I agree that this model heavily encourages the developer to design around that methodology (well described as "gamed" above).
To be fair, in this specific example - if I recall in Triple Town, the main thing you bought was unlimited play-time ("turns") for $3.99 (which follows the more positive unlock model). After that you could buy the standard coins (the shitty model), but given the design of the game I never understood why you would.
Even buying champions in LoL (you can buy skins too) doesn't affect the game really because every week the champions you get to play for free rotate, giving everyone a chance to play whichever they like and secondly, they are balanced so that it doesn't really matter which champions you play if you're skilled. You are really paying for a different experience.
So, the three models of free to play that I see are:
1. pay for perks - this is the traditional "you pay and you get something you can use", be it guns or coins or whatever. The danger with this model is that it is a very fine balance to prevent this from becoming pay to win.
2. pay for cosmetics - DotA 2 or skins in LoL or hats in TF2 or whatever you have. Buy things to change the look of your stuff in game, but buying things has no effect on your success or the gameplay. IMHO almost all free to play games should support this in some way.
3. pay for experience. The things you buy in game don't give you an advantage in the game but instead alter the play style or how you experience the gameplay. League of Legends gives you weekly tasters of the different gameplay experiences the different champions have to offer and you can pay to keep the ones you like best. I believe that this is the model (coupled with #2) that ultimately makes the very successful free to play games stand out from the merely moderately successful ones.