Stuff like the ATmega chips run the application barematal, yes, but they are cheap microcontrollers with 2KiB of RAM and no MMU. You can't run a kernel on that so your application runs bare.
A lot of the higher-tiered embedded stuff usually either runs a Linux kernel or DOS (and older) from my experience.
Systems running Linux are the exception.
Linux does not fulfill the security requirements of high integrity systems nor the real time constraints.
Embedded systems running Linux are extremely common, and becoming more and more popular because it runs on so many architectures (esp. ARM, but also PPC). For many applications, hard real-time is not necessary, and Linux is FAR easier to develop on.
They are not "the exception" by any means. Look at almost any automotive "infotainment" system on current models: it's likely running on Linux. There's countless others.
For high-integrity systems for critical safety applications, you would not use Linux, you'd use a dedicated RTOS, of which there are countless choices. But these all have big disadvantages: poor performance (they favor determinism over performance), poor development support, high license costs, etc. If you're doing avionics, then sure you'd use an RTOS, but if you're making a "smart TV" to play Netflix, you wouldn't, you'd use Linux.
Also, Linux does have real-time capabilities, it just isn't hard real-time, only soft. It works well enough for controlling hobbyist-level CNC machines. I've used it myself for a pretty critical real-time system where ease of development and performance were more important than absolute real-time guarantees.
This means you also have no numbers to back up your claim.
https://m.eet.com/media/1246048/2017-embedded-market-study.p...
Apparently I was wrong, see it wasn't that hard to find.