A $75 bottle of wine tastes better than a $14 bottle of wine. Even if you switch the wines. The promise implied in the price actually changes the way we experience the product.
Two things to keep in mind:
a. Giant promises lead to poor experiences. When you strain credulity and then fail to deliver on the miracle, we won't enjoy it, nor will we trust you again any time soon.
b. The reason we hesitate to make big promises is that we are afraid. Afraid to own it, afraid to be vulnerable in the face of possible disappointment.
Once you make a big promise, you have to work harder to keep it. Easier, it seems, to merely make tiny promises instead.
But the fact remains: Human beings have better experiences when they expect to have a better experience. To hold back on your promise is to deprive your customer of something valuable.
A promise doesn't have to be a grandiose statement, with or without fine print. It can be something as subtle as the music you hear when you walk into a restaurant or the respect a salesperson offers you when you first interact…
[I'm going to disagree with myself about a different sort of case–it is the promise that starts an ongoing experience. A promise just big enough to get me started on something that gets better all the time is the best way to engage, because that ever-improving experience will continue to delight and surprise, increasing my word of mouth and satisfaction. Alas, these sorts of experiences are hard to build and hard to find.]