^^Interesting to read of your perspective, Harry.
I never thought of "Sing" as a 'novelty' song (i.e., it's not Goofus).
While the song appears simplistic...I believe appearances are deceiving, in this instance.
The arrangement--the entire arrangement--is, as I've often said, brilliant.
I've always admired the duo for having the guts to record and release the song as a Single !
I respect your view that it did the duo "no favor as far as their image went."
Perhaps, as of mid-late 1973 they were having those "image problems,"
however, the brunt of those image problems--in my opinion--really snowballed in 1976.
The July 1976 People Magazine Cover, and article, did them no favors.
The First 1976 TV Special--as highly rated as it was--did them no favors.
None of the Singles: Hush, I Need To Be In Love, Goofus....1976....helped their image.
I simply see nothing in 1973 which compares to 1976, in terms of "image."
August 11,1973 (Billboard,page 17,Talent In Action):
" The Carpenters may be a bit too saccharine for some, but, judging from the avalanche
of applause they left the stage with,Karen and Richard would be foolish to tamper
with their G-rated approach to music."
There can't be any argument that from a purely commercial point of view in the sense of 'what's going to be the next hit?', they were obviously on the money with 'Sing'. It did well and, as has been noted, better than say 'Goodbye to Love', which is rated more highly by most fans and critics.
However, I think there's a case to be made that rather than judging things merely on the basis of 'what will be the next hit?', they might have been better off picking at least some songs that would challenge the image that had ben built up of them and that might allow them to challenge perceptions and start appealing to other demographics.
The Billboard writer Paul Grein, a long-standing supporter of the Carpenters, wrote some insightful pieces in the early 1990s on why the Carpenters ran into trouble in terms of their image and subsequent chart decline. He mentioned 'Sing' in particular as a misstep in this respect - a quick sugar-rush of a hit, but without any longlasting benefit to their career and a track that would be used as evidence for years to come for them being a lightweight act that didn't deserve to be taken seriously.
Whilst 'Goodbye to Love' didn't go gold, it did cause some critics to take notice of them and it's a track that's still talked about with some reverence now by many critics. It didn't achieve their short-term aim of getting another Top 3 single, but in the long term it's more than justified its release as a single - it helped to change perspectives on them. I believe that releasing 'This Masquerade' in 1973 could have done something similar - it didn't sound like their other singles (or even the other Leon Russell songs they'd recorded), but it had real depth to it too. Again, it's a song that's often singled out by critics as one of their best performances. Instead, we got 'Sing', 'Yesterday Once More' (a favourite with some but not a departure from their general sound) and in some countries 'Jambalaya' (which was almost as lightweight as 'Sing').
Of course, the image problem wasn't just down to releasing songs like 'Sing' as singles, but it certainly did nothing to help matters, and it's one area where I think they had some responsibility in adding to the problem. Their fans may have lapped it up in 1973, but once the market starting turning against them, those fans weren't buying their singles anymore and they hadn't done enough work when times were good for them to show the audience that there was more to them than the 'saccharine' image suggested. As such, there was very little they could do - they weren't having hits with their trademark songs or with more challenging material like 'Calling Occupants'.