Brisk-sg said:
Component Input is important only so far as it allows for superior picture in comparison to RCA or S-Video. Also, Component is one of two standard connections for High Definition Inputs/Outputs. A Component Cable is actually three cables, one for each primary color, allowing for the best color depth and clarity.
Actually, the three Component cables are not "one for each primary color" -- even though they're coded that way. Component is not the same as RGB. Component video separates the signal into three channels - Luminance (black/white) and Chrominance (red/green difference and blue/green difference).
Component IS the highest quality analog video interconnection, though it's likely to be trumped by DVI in the near future.
The reason Tivo doesn't have component outputs is that it likely wouldn't result in a better image. Tivo records off-the-air or off-the-cable/satellite programming, which is either low-quality analog or heavily-compressed digital. With the exception of HD channels, a standard broadcast (regardless of medium) will never have the color resolution necessary to make component connections useful.
The only benefit to component outputs on a Tivo (or similar) would be the inclusion of de-interlacing circuitry to produce a 480p image from the 480i source. Of course, there are plenty of out-board products to do this (they're called "line doublers"). Keep in mind also that only digital sets can produce a 480p image -- and the presence of component inputs does not indicate a digital set.