Short answer: because it is cheaper. Ads that show a puzzle the game barely contains often get more taps and cheaper installs than ads showing the real game, and the companies buying the ads are judged on what each install costs. Here is how that happens, what regulators have said about it, and where you can actually play the games from the ads.
You have probably seen at least one of these:
They often carry a banner like “99% FAIL THIS” or an IQ score, and the player in the video usually gets it wrong on purpose. Then you install the game, and the main game turns out to be something else entirely, such as a match-three puzzle, a city builder or a strategy game.
Mobile games are mostly marketed with paid ads, and the number that matters is cost per install: how much the studio pays for each new player. Studios test dozens or hundreds of ad videos against each other, some honest and some not, and keep whichever brings in players for the lowest price.
Ads with a simple, unfinished puzzle tend to win those tests. A player who watches someone fail an easy-looking puzzle wants to try it, so more people tap the ad. Many of those players delete the game once they find out it is different, but if enough stay, the maths can still work out for the studio.
Some of these ads also began as concept tests: a way to see whether a mechanic attracts players before anyone builds a full game around it.
It depends on the country, and ad rules are usually enforced case by case. The best-known decision came from the UK. On 30 September 2020 the Advertising Standards Authority ruled that Facebook ads for Homescapes and Gardenscapes were misleading. The ads showed pull the pin puzzles; the games are mainly about renovating a home or garden and playing match-three levels.
The publisher, Playrix, argued that pin puzzles had been added to the games in an April 2020 update and that the ads carried the line “Not all images represent actual gameplay”. The ASA was not persuaded: it found the ads were not representative of the games overall, and told Playrix not to run them again in that form.
This is general information, not legal advice. Rules and enforcement differ between countries and app stores.
As the Playrix case shows, the puzzle from the ad sometimes does exist in the game, as an occasional bonus level or a mode that unlocks later. That is why some ads carry small print about images not representing actual gameplay. Technically the puzzle is there; in practice you may play for a long time before you meet it.
Some studios have since released real games built around these mechanics. We made two: The Real Fake Ad is the pull the pin puzzle from those ads, and Save the Dog is the draw-a-line bee puzzle. Both play in your browser with ten levels, no install and no app store.