A product for everyone?

It is perhaps a sign of my own business naiveness that, before business school, I thought the goal of any business should be to gain as many customers as possible. Why not try and convert as many people as possible into one of your customers? Isn't that the essence of marketing and sales -- to create as many customers as possible?

As I learned in Prof Grayson's MKTG430 Marketing Management class, sometimes it is better to target a small number of people in a market, creating a more valuable product that this small segment is willing to pay a larger premium for. Revenue is, after all, price x units sold. It is easy to get caught up with trying to figure out how to maximize units sold, when perhaps instead we could be trying to figure out how to increase price. What would you have to add or do differently to compel customers to want to pay higher a price?