I've seen such displays, often using separate LEDs for each color as you intended... however, they are generally very large signs (5 feet tall and 8 feet wide or more) and they only look half decent at a distance... and even then you can clearly see the separation between colors in each pixel.
Whether you use single package RGB LEDs, or use individual LEDs, the cost is bound to be astronomical... RGB LEDs are often a few dollars apiece, and I doubt you could easily find them for less than $1 each. individual red and green LEDs are a dime a dozen, but blue ones can be expensive; and most likely for a project like this you would want the LEDs that are clear in the off state, which are usually more expensive as well. By the time you get an array big enough to display anything interesting, you'd probably be looking at a few thousand dollars worth of LEDs, and needing a whole lot of lines to control them. I think you could do plenty of interesting things with a single-color dot matrix LED display, in which case you could probably be fine with run-of-the-mill red LEDs, which you can get for as little as 1.5 cents apiece quite easily.