In Gumshoe One-2-One, a push is defined as a resource you use to influence the investigation towards more than just acquiring information for your investigation. Examples include blackmailing a suspect (who you would normally just question), reminding a contact owes you a favor for saving someone's life (when they'd normally just provide minor support), or finding a hidden compartment from information for bailing a witness (which you normally wouldn't find), or other such things.
But investigation skills automatically succeed for you. There is no failure, as long as the player uses the appropriate skill in the right environments. Even if they do fail to acquire something, the game suggests you discreetly give it to them anyway if the information at hand is important. Pushes are rewards for taking risks during Challenges, but they don't improve future challenges or help you avoid Problems.
In addition, Gumshoe One-2-One is defined as a game played through excessive preparation, and to rely on improvisation as little as possible, but Pushes are strictly improvised uses, to move the story in unpredictable ways, which can cause the story to become clunky for both the GM and the Player. And these are considered very limited rewards. You start a module with 4, and you basically get more from critical successes.
You could risk breaking a limb or going insane during a Challenge, which could definitely cost you, but the Push you get as a reward grants you...slightly more information that you normally would have gotten, in a game where information is just given to you? When I could have gotten an Edge, which could be used to succeed on a future challenge and prevent me from going insane.
I kept reading into the book, waiting for it to tell me how to use Pushes effectively, but...nothing! No recommendations on how to use Pushes to avoid dangerous scenes (like avoiding a bad-to-worst fight with a Shoggoth), no mention of using a Push to give you more time, which might allow you to Take Time to recover from some of your Problems. These are things I can Improv, but the game recommends not improvising much, to avoid putting the story in a hole that's awkward to get out of.
A Push can be used with an investigative skill in a scene, and the Player's Character has about 10 Investigative skills...that's a lot of possible uses for a Push, if an average scene lasts 15 minutes of play.
How am I supposed to use these? Am I (The GM) just supposed to come up with different paths for every single possibility for every scene and every possible use of a push?