I worked for a certain large online retailer for several years. I can tell you there's a continual back-and-forth going on between retailers and manufacturers on the issue of Minimum Advertised Price (or MAP). It's literally discussed at almost every meeting with a manufacturer. A few years ago, letting customers click to see the price instead of adding to the cart was quite a controversial idea among manufacturers, let me tell you.
Retailers want to show the price to consumers as early and often as possible, and they want the flexibility to aggressively discount when it serves their purposes, even though this cuts into their margins. The main motivations: matching a competitor's price or needing to reduce inventory.
Manufacturers, on the other hand, believe that advertising their product below a certain (totally arbitrary) price threshold will degrade the perceived value of their products and ultimately degrade their entire brand. They're quite superstitious about this. They constantly talk about Price Erosion - more on that later. In essence, manufacturers try their best to maintain artificially high prices on their products for as long as possible, and one way to do this - they think - is to keep perceived value as high as possible by hiding prices. Convoluted logic for sure.
Retailers are not legally required to hide the price, but as you might imagine, continually defying manufacturers' wishes does lead to repercussions. Amazon, Newegg, and the rest know that hidden prices are a bad customer experience so they try to strike the best balance they can. Lately, that's taken the form of click here or add to cart to see the price.
Price erosion is a natural phenomenon during the lifetime of many consumer products, unless supply is constrained or demand stays high. Some companies have built such strong brands that they rarely need to worry about soft demand. This makes their products virtually immune to price erosion, and as a result they don't need to hassle retailers about MAP. Apple is a prime example. Retailers rarely need to cut prices on an Apple product in order to get it moving off the shelves. Why? Apple has a reputation for high quality and better overall user experience compared to the competition. It turns out people are willing to pay more for this. Shocking, I know ;-)
EDIT: Hiding Price to Increase Demand
There are actually times when this will work for a little while. Usually on products that have a lot of price volatility. The theory is that we've gradually acculturated to think hidden prices imply higher value. But it's the exception to the rule. As a manufacturer, you're much better off building a good product than trying to play little games with the price.