Excuse my ignorance but as far as I know, SLR was invented in order to get the photographer to see (through the viewfinder) exactly what image will fall on to the film. In digital cameras the image falls on the CCD (or whatever type the censor is) and afterwards the image is transferred on the LCD in real time. In other words, you don't actually need a viewfinder since there is the LCD screen of your camera and you see what image will exactly fall on the CCD. Am I right in my thinking?
I suspect the major reason this is true for DSLRs is to get the lightning-fast focus times that point-and-shoot cameras don't have. The autofocus mechanism is not actually part of the main CCD/CMOS sensor, but a separate device in the camera body, and the mirror splits the light coming through your lens so that half goes to the viewfinder and half goes to the autofocus sensor. See, for example, this site describing the differences between a mirrorless camera and a DSLR; note in Figure 1 the autofocus module below the mirror.
This autofocus module is doing a phase detect autofocus, which is extremely fast. Without a mirror, you have to do contrast-detect autofocus, which is slower. Recent cameras (e.g., the Sony a55), have gotten their autofocus fast enough that they no longer need a mirror, but it's taken quite a long time for the technology to get there. So I suspect the trend will be towards cameras with DSLR quality and focusing speeds, and no mirror (perhaps with an electronic viewfinder, instead). But it's only been recently that such things have become possible.
The best answer I can provide is MILC article on Wikipedia. I'd add power consumption to the list of drawbacks - using an active viewfinder/LCD screen requires current delivered to the sensor and of course to the display.
You have just invented the mirrorless inter-changable lens camera. SLRs were needed because back then, in the 60s and early 70s, there were no electronic viewfinders. Things like the Nikon F were amazing and advanced.
Some people prefer the pentaprism viewfinder, but that is just a personal choice. With a good electronic viewfinder, cameras can be lighter, smaller, and perhaps even cheaper.
I guess it is about the "true-ness" of the captured photos, I.e. whether a photo is exactly like one that captured in film. Although it's true, like you said, that all digital cameras offers the SLR viewfinder's effect, only DSLR's give you the best images thanks to the use of much much bigger sensors than a casual point and shoot.