To clarify on my comments because I believe there is some misunderstanding. A super expensive, high end, professional full frame camera is considerably more capable than a consumer level crop camera. The issue is not everyone can afford a super expensive high end camera, therefore crop sensor cameras exist in the market.
You're mostly correct, but to be fully correct, you should acknowledge the process of how "crop" sensor cameras came into existence in the first place.
I will tell you.
When digital photo sensors were first introduce into the consumer market, the cost to produce sensors was such that the 35mm sensors were substantially more than for smaller sensors, so camera manufacturers introduced "crop" sensors to the consumer market to sell more cameras.
Naturally, camera manufacturers would like to keep on promoting their "professional" cameras and charging more money for them, so there is the marketing strategy of maintaining different lines of cameras.
Therefore, they put more technology into the "professional" lines to keep prices up, even though the same technology could be put into the "crop" bodies for only a little more cost. See the Nikon D500 for example.
Actually....
The first digital SLRs were full frame.
The Nikon and Canon DCS in collaboration with Kodak were all full frame.
The Minolta RD 175 was also full frame.
The reason why the sensors were cut to APS size was because of the silicon wafer industry.
Silicon wafers that make the sensors in digital cameras have their origins in the old round solar panel designs from the early 1980's The wafers were originally round because they are grown as a crystal structure in long tubes.
These tubes typically are around 6-10 feet long and were a standardized 6 inches because the grown crystals had integrity issues beyond that size in the beginning and also because the wafer industry was not involved or concerned with photography.
The typical size of silicon wafers are cut from an ingot that was a standard 6 inch diameter. You can cut 4 35mm sensors from a 6 inch round with a substantial amount of waste.
With APS, the amount of waste is greatly reduced and the number of sensors cut from the 6 inches is higher than with 35mm.
The APS size was chosen because of the leftovers from the Advanced Photo System (APS) debacle.
The equipment was cheaper to hold onto and the original glass was all for full frame sizes and trying to retool the 35mm side of things for high production didnt make sense.
There are many who believe its impossible to create a full frame medium or large format sensor, but its simply a matter of tooling.
In regards to the image quality between FF vs. crop, what MUST be remembered is that the MOUNTING DISTANCE is the same in both for such camera lines as the EOS and Nikon. The glass focuses at the same focal distance because its easier and cheaper to produce such.
Hence, the image produces is exactly the same because it IS the same, because the FOCAL DISTANCE and MOUNTING distance is the same.
The only reason why we have this stupid argument is because many simply do not grasp the concept that the 'crop" is actually delegated by the reproduction ratio.
If you mount say an EOS 100mm lens on a Canon 5D (full frame) and that mounted on a tripod, take a picture of a car, then switch the camera out to a crop sensor, but use the same exact lens and the same exact distance, the image in both cameras are exactly the same. Then take the picture with the same exact distance without re framing, and voila, the "crop sensor" image must be enlarged more to equal the same reproduced image from a full frame image on a 4x6 or 8x10 print.
The economic advantage simply came along for the ride.