Reddit mentions of Games As A Service: How Free to Play Design Can Make Better Games

Look up Oscar "the hat" Clark
And "games as a service"
http://www.amazon.co.uk/Games-As-Service-Design-Better/dp/0415732506

for me this sound more like you are looking for useful monetization of your game. In that case there are several general approaches you can do:

1. Premium - not really option for mobile market, because it is crowed with tone of games, it have high barrier to entry and I presume that you have no marketing money - would not recommend
   
2. Adds - very useful way how to monetise mobile game. People are used to that. It is easy to implement (basically add API and put in on right spot in UI)
   
3. IAP - as you already mentioned. There are several things that people may pay for (and why):
   
   1. Social proof - showing other that you are good enough or better than others. This is exactly why people would use things like loolipop hammer in candy crush or customization/ skins in games like overwatch or farmville. To this to work you have to allow player to show off - leaderboards (check mini metro), comparison with friends (How candy crush do it)
      
   2. Achievement - People like to accomplish things. If you manage to put things in certain patters for example in bunch of levels of 5, where 3 are ok, one is hard and one is almost impossible player will very likely pay for booster to complete last one.
      
   3. Limited offer - some boosters may be useful only limited time (or have 3x the power or smtg)
      
   4. quality of life - getting rid of adds, shorten timers, more effects
      
   5. compulsion/habit/chance - you seen this, for example loot boxes. If booster means that they can possible get points then they will buy it (again candy crush is master of this, but also homescape and gardenscape)
      
   6. ....and many more
      
      Understanding player motivation in this case is the key as I believe you already know. I don't know exactly what you game is but there is bunch of places where you can find your more about how to monetise it (and yes it is not as easy as to put there some IAP)
      
      Check videos from Casual connect.
      
      There are several good books about this: Game as a Service by Oscar Clark or The Curve by Nicola Lovell
      
      Also you can check out free to play bible with lot of advice.
      
      In the end you wrote want thing that I want to highlight: " If the game can be enjoyed for free, meaning levels don't feel impossible, why would someone spend? " Well, they don't. If you don't make your player to pay they will not.