I am talking about this :
Are there some psychological reasons for not displaying the amount user is paying on the button ? If not, then why don't I see it anywhere ?
Well it's not a completely unused pattern:
I see this pattern mostly used where the purchase button is the only step in the process (that or purchase button + sign in/password). This is how Google Play, iTunes/the App Store and Amazon's App store all work. Note the following about all of these stores:
Another thing to note is "pay $240" is just the means to an end; I didn't go on your site to spend $240, I went to your site to order something. So "place order" or "checkout" is what I really want to do; hence why iTunes uses the copy "Buy" instead of "Pay"; payment is implicit and expected.
Checkout/place order also have the benefit of fitting the model of a store transaction; you grab your items, then you check out or place the order. The Shopping Cart model (for better or worse) strongly follows the physical checkout model, and I suspect the metaphorical copy is also tied to that. The app stores are a bit more modern and simpler, so they can get away with just "buy this one thing".
I'm not sure I could say there's any one reason to not list the dollar amount on the button, but I do think there are good reasons to put the dollar amount on the button or to not do it. If your shopping cart and price labels are implemented clearly enough, there really shouldn't be Sticker Shock if you put the price on the "pay" button. The standard shopping cart method may be a bit overly complex, but it does afford users multiple confirmations of the total price of the cart before you hit the big "pay" button.
Perhaps counterintuitively, any time you think Sticker Shock might be an issue I think you should put the price right on the "pay" button; take Uber as a case study in unclear pricing. In the long run angry customers can cost you a lot more than a few people turned off at the price.
You should always let the user know the price.
As for why you don't see it on the button: The price is typically present somewhere else on the page ( I'm thinking in terms of ecommerce ) very noticeably. It may just be redundant to have it on the button as well. That's my opinion, at least.