First off, Polaroid photographs don't necessarily look like the "Polaroid effect". It depends on which Polaroid film/process you're talking about, and how the pictures were handled and stored over the years. Photographs made with the SX-70 process are probably second only to Kodachrome transparencies in dark-storage colourfastness (although they tend to have cracking and crazing problems due to over-hardening), and the wet-wash Polaroids from their extreme large-format cameras (like Ansel Adams' official in-office portrait of Jimmy Carter) are showing little sign of deterioration.

The "Polaroid effect" tries to reproduce the look of the classic peel-apart Polacolor print of the 1960s. That particular process resulted in prints of relatively low contrast and saturation to begin with, since there wasn't the complete separation of negative and print that there is in most other processes; there was some density from the negative image in the highlights of the image, along with some clouding of the colours. (That was unavoidable. In other colour film processes, whether print or reversal, the light-sensitive silver compound is completely removed during processing. Polaroids didn't go through a liquid bath that could wash the silver away.)

Like most colour processes of the time, the colours themselves come from organic dyes. (That's organic in the chemical sense, not in the "no Monsanto" sense.) Almost all are prone to fading in the light, and many are prone to oxidation. In addition, there was always a slight contamination of the print with the processing chemistry, and that chemistry was rather reactive. Properly "finishing" a Polaroid print meant varnishing it to retard oxidation, and that didn't always happen. Most of the Polaroid photos were taken in the field or during functions, and the photographer often had better things to do at the time. Oxidation of the dyes is one of the sources of the "classic" faded Polaroid look.

The other is exposure to light over the years. Even though that may simply mean exposure to artificial light in the home for a framed photo, we are now talking about fifty to sixty years of exposure, and that's a lot for any photo. (Even conventional photos from the period often show a good deal of light fading.) Each of the dyes has its own lightfastness, and organic reds are generally more fugitive than other colours. (If you've ever been somewhere where there is very old litter lying around in the sun, you may have noticed that red things, like Coke cans, tend to have discoloured more than greens or blues.)

From the mid-seventies onward, there weren't many people other than professional photographers using peel-apart Polaroids. The consumer instant-print market had gone to the SX-70 process and cameras. Professionals used the peel-apart film to test exposure in much the same way that digital photographers use the LCD screen on the backs of their cameras today. Call it prehistoric chimping. In any case, the pictures that resulted were just a check on (usually flash) lighting, and not the final product. With neither consumers nor professionals particularly interested in the longevity of Polacolor prints, the process never saw any major improvement even as more lightfast dyes were being used in other films.

Polacolor pictures that were properly varnished and stored in the dark (like in a photo album or a shoe box in the closet) tend to be very close in colour to the way they were originally, showing only a little bit of fading from oxidation of the dyes. (Again, we're talking about a half-century of exposure, so you can expect some aging.) The "Polaroid effect" essentially reproduces the fading that occurs in unvarnished prints that have spent at least a good portion of their lives out on display.