Im not sure there is much of a public perception of karate.
There is the constant onslaught of movie and tv karate that has no relation to reality.
There is some awareness of karate schools (especially those schools that give public demonstrations often perpetuating the same mythology about karate) and if a family member participates they may have seen some tournament karate, most often point sparring. But on the whole the public neither worries about karate much and most often sees it today as a youth activity just like dance classes.
BTW, today on Okinawan 75% of the karate students are youth too, from about 0% in 1972. Todays perceptions are often a world wide situation.
Lets look at it clearly.
Pre 1900 there was almost no karate, just a small group of private practitioners. There was no sport version of sparring. There was almost no violence on Okinawa that required karate-ka to defend their families. They were part of the Japanese empire, and karate developed by members of the elite classes for their own reasons. Almost the only thing we can say for sure is that the primary training tool was kata, and what practices were wrapped around kata study remain speculation.
Post 1900, there was some transfer of karate into the Okinawan equivalent of high school to prepare young men for the draft into the Japanese military. Only the elite sent their youth to school at that time, and the primary purpose wasnt karate for self defense but for drilling practice to prepare them for boot camp.
Most Okinawan karate remained in small groups of study, but as time passed and the depression continued to hit Okinawa hard, more and more instructors tried their hand at training youth in school or after-school programs. There was some experimentation of sparring with Kendo gear but it did not become a universal practice, and karate remained primarily a kata study with subsidiary practices.
Karate also was exported around the world. First in the Okinawan disporia from depression, too much population not enough land, to communities that developed throughout the east (Singapore, Japan, etc.), Hawaii, South America. We know little about who did what.
More formally Karate spread to Japan into the University system, and it was organized for the needs of University students. As Japan was a civilized country it was not primarily done for self defense but hard adult training. In time the University system developed a way to practice sparring with a handful of karate techniques, and after WWII, this was exported to the world. In the USA those practices, with many variations, developed a wide range of practices. There never has been one universal sparring approach in the sport developed. No contact point sparring, light body contact point sparring, hard body contact point sparring, semi-pro sparring, full contact sport sparring, etc.
Then government regulation took hold. They looked at the growing karate industry and many states wrapped it into the Health Club industry requiring bonding insurance. That brought the insurance industry into the controlling hand. And sparring without very restrictive practices and full body gear became the rule to keep the insurance.
So point sparring was the logical conclusion as the insurance industry does not exist to pay out money.
Other sorts of sparring exist outside of that control, and PKA, or those who want to compete in MMW, whatever, exist too.
But the existence of sparring is a modern phenomena, and how far it goes depends on each groups rationale.
It is safe to say most people who practice are not doing so to risk injury playing any variation of a game, and will not compete. For those who do compete in harder and harder contact, there is not any public analysis of what the long term impact of those practices have on ones health in later years. They are mostly doing so at their own risk.
Separate has been the study of Kata technique application, the Japanese term is bunkai, but there was not a clear Okinawn term for such, as most of their practices were without any technical vocabulary, theirs was a non-verbal form of transmission. BTW the term bunkai is a specialized usage in some but not all Japanese systems and its public usage is very different from its karate usage.
The potential range of any techniques application potential is often very vast, but as much of that usage will cause great damage to a partner, it often must be practiced slow and in a restrictive manner, allowing kata to be the training tool to learn how to develop full force. How any system or school approaches that study is their choice.
Technically one technique that can respond to any attack is theoretically all one ever needs. The larger study then becomes a growth for the practitioner potential.
There are a lot of valid ways to practice arts that are effective, but if they are a descendent of Okinawa karate their primary practice is kata. If it is not kata ,then it is something else, worthy but not karate, IMO.