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Players roll the dice, and wait to see the landing. Like roulette, football, or anything else, the pay-off emerges when they physically see the result, and know in that instant, how things have gone. They get a moment of tension, then relief, or panic.
Having an unknown Target Number (TN) moves the results away from the rules, and gives it to GM fiat. Instead of a jump going how players think it should, the jump goes as the GM decides in the moment. The tension is stretched, as the players see a '12', think '+5 is 17', then look to the GM, who often won't have made up their mind before the roll came in. However honest the GM wants to be, the GM will always feel tempted to not put down the effort to make a decision.
Adding GM fiat also creates a second layer of randomness. RPGs need randomness to develop an emergent plot, but they only need one source. A few games run by GMs keeping target numbers secret already, and removing any need for dice. The GM might write down a hidden TN, or place a pile of hidden tokens to mark the TN, then have players spend 'Determination Points', or 'Luck Counters', and reveal who's passed, and who hasn't. The guessing-game of counters works fine for randomness in diceless games, but adding dice to guess-work makes the world too murky.
For situations where players cannot know the TN - where they research a fact without knowing how long it will take, or try to bribe a guard without understanding the depths of his loyalty - the GM can simply declare a high TN, and expect the player to roll, even with the high TN.
You begin asking if there's another way to do this. The guard notes this sounds like an illegal proposal. Target number 16.