Can any one point to Why Image problems might have arisen?
That's easy. Just look at the pictures from their first 10 years in the limelight, and compare with any other young acts of the day. The problem was, nobody knew how to market them since their act had kind of an unusual configuration (male/female, but they were brother and sister, as opposed to a "couple.). Plus that was a time when the "clean cut" look in young entertainers was going by the wayside...compare a picture of the Beatles in 1964 to a picture from 1970 and you'll see what I mean. So combining their visual image with their overall sound, the Carpenters came off as too goody-goody. Doing "oldies" and songs like "Goofus" didn't help. Then if you listen to audio interviews from the time....well they really come off as kind of nerdy, if that makes any sense. If you were a young kid at the time, they seemed like young versions of your parents.
I was 24 when "Close To You" became a big hit so I could totally understand why they had image problems. The problem was, given their style of music, there was no real way to get out of the problem because if they'd tried to look like a couple of hippies, it would have come off as phony. They looked like they looked because that's who they were.
Plus, when the image problem really became noticeable, instead of even trying to look more "hip" they went the other direction with the A Song For You album, packaging it up like a Valentine card. It wasn't until Horizon that they really tried to come off as modern young people, rather than the Hallmark version. By then it was too late; the music had evolved to an even LESS modern, easy-listening style (especially with songs like "I Can Dream Can't I"). By the time they did Passage, their biggest effort to change their image (even almost-ditching the famous logo), the public's perception of them was cast in stone and they were forever doomed to be "un-hip."