There are games like those you're looking for but they use In-app purchases (IAP):

Games with ads and that are incomplete, where you purchase the "complete game with no ads" with a single purchase.

So it's like a demo that you upgrade to full version.

The problem is that because there's no "demo" functionality in the app store, they get labeled as games with IAP which turns many people, me including, away.

Before IAP, there were Free and Full versions of the same game (with and without ads and other perks), like Angry Birds and others.

If they made a "demo" category where the game has ads and fewer levels, or limited play time that you could upgrade to full game without ads, I'd be much happier as a dev and as a consumer.