They do solve a problem. They may just not always be problems that we can relate to. Keep in mind that we all have different needs/problems. And emotion can play a part in the kind of problems we have and how we solve those problems.
As to why luxury items can be sold for high dollar amounts: because people will pay for them. Some people have more money than they can spend in a lifetime, so why not splurge on high end items. Others may feel pressured into buying expensive items if those around them do so. The human mind is complex, and there are many reasons why people buy luxury items. That's why it pays to understand your market and their needs. If you can offer them what they want, you can charge a premium for it.
Take for example designer clothes. A simple problem like "I need something to wear to the party next week" can be solved in many ways. It's up to you to know your audience and get inside that person's head to offer them the right solution.