In '72, about 1 in 8 new C3 owners ordered a 4 spd. For my year, '79, only about 4K out of 53K sold ordered stick shifts. That's not a very impressive/sporting ratio compared to, say, Porsches or BMW 3-series when both autos and sticks are available. (Good news for the resale value of my 79, though, maybe.)

I think it was for a number of reasons.  The market was changing and the Corvette changed along with it.  More people wanted comfort and a/c...and automatic trannies went along with that boulevard cruiser image.  I believe it was early in the C3 run that coupes started outselling convertibles.  Fewer engine options became offered...some because of Federal emissions regulations, some due to insurance premiums increasing.  

I don't know if the buyers were getting older, but it did seem like the trend was for personalized luxury cars. In the case for Corvette is was luxury/sport. As Gunslinger wisely pointed out convertibles were going out.........the "T" top kind of helped to diminish the convertibles. I had three Corvettes in the 60's. All were the highest horsepower available. All had 4-speeds. All had 4:56 gears. Corvettes were for die hard enthusiasts, true lovers of fast sport cars. By the time the 70's rolled around, the buyers were a whole different breed. I noticed that doctors and lawyers were now into Corvettes. They didn't even wave when you would pass by. The new clientèle wanted all the luxuries. During the 60's it was all about performance options. AC,  power steering, power brakes, power windows etc were for sissies. Fast forward to now......... everyone wants the 4-speeds and big engines  

Yeah...as the Sharks aged, the "focus" of the buyers changed, also. By the mid-'70s, buyers were getting away from the pure horsepower cars, and going more toward cruising, and GT type cars. Plus, it was much harder for the manufacturers to emissions certify standard trans cars...still is that way today. The Corvette was putting on weight due to the gov'ment crash requirements, and emissions requirements were killing the hot engines...folks really didn't have much choice but to go with the GT style Corvette...ones made more for touring in comfort than blasting down the drag strip. GM was sellin all they could build like that, so it must have been the right decision, AT THE TIME.
My '74 is a 4 speed...the '85 is auto. Two different cars, for two different purposes.

I've never been asked by an insurance company what transmissions the cars I wanted covered had. I wonder if your experience or mine is more common.

I think the differences are age related. CCasey was 27 and Bill I'm figuring that you are older than that. Years ago, if you were a male under the age of 28 (they kept changing the age) the insurance companies frowned on muscle cars.

No, I was in my 20s when I bought my first C3 and early 20s/late teens when I bought a 403 Trans Am. They never asked about transmissions, but CCasey bought his new and I got mine used. Maybe that makes a difference in how much info insurance companies ask for.

Back in the '60s and '70s, a young person had a much harder time getting insurance than an older person, due to less experience, and usually, the younger person wanted a hot car...not a stodgy Oldsmobubble. An 18 year old buying a new L-71, or other high performance car had to pay a really high insurance premium, IF they could find an insurance agent that would cover them. A 30 year old, buying the same car, would pay less, but still more than if they were buying a 6 cylinder Impalla. A high performance car with a 4 speed would most certainly be used for "improper" things such as drag racing...or...horrors...STREET racing!  Street racing would inveritably result in an accident of some sort...so that's why the insurance folks wanted to know what kind of car they were insuring....Granny in her 6 cyl Biscayne driving 25mph would do a lot less damage than Johnny Racer with a '67 L-88....

I wish I could remember what the differance was in the premiums for a 4-speed vs an automatic but I do remember that it was significant.  (The issue of type of transmission seemed to only applied to "muscle cars" as I remember, not to all cars.)  I was single at the time, which also added to the cost of insurance.