This exactly. I've been playing a lot of smartphone apps recently. I have no trouble paying something for a game. If they want to release a "lite" version with limited levels, I'm fine with that. It lets you get a feel for the game play and see if you want to spend the cash for the full version. I don't even have a problem with additional level packs costing more money. What I have a problem with are games where you either 1) Need to buy items with the "premium currency" (only obtainable by paying cash) to advance in the game or 2) Need to pay to keep an "energy meter" up. In the latter case, if you limit how much I play your game, you are just making it more likely that I'll play another game, not pay you money.
As an example of a game-gone-wrong, I'd submit Where's My Water. The first game was pretty good. There was a lite version, a paid version, and additional level packs you could buy. Then Where's My Water 2 came out. At first, they had an energy meter, but they got rid of that when people complained. My big issue? Keys. You can only obtain keys by 1) buying them or 2) bugging people on social media. If you don't do that, you can't proceed along the map. If you buy the keys, you will just get stuck at the next gate that requires more keys. So you aren't even buying "the full version", you are buying "the next level or two." The end result? I don't even have that app on my phone anymore.
I don't begrudge game developers from making money, but it's a fine line between encouraging payments and annoying people too much.