Coaxial helicopters do exist - in massive numbers (they're just tiny)
Coaxial helicopters do exist in massive quantities - but they're just tiny little things.
What am I talking about? Well, I fly RC helicopters ... and in the world of RC helis you can't get away from coaxial stuff right now. If you have an interest in flight and in particular helicopters you absolutely should go out and bag yourself a cheap coaxial helicopter and start getting away from 'virtual' and into real flight.
This is a big topic and a fascinating one as far as I'm concerned. RC manufacturers are not bothered with the politics of Kamov vs. Mil vs. Sikorsky - they just want to build something that can be mass-produced cheaply and people can fly well. As such a large number of them have settled on coaxial machines as entry-level helicopters for RC control.
You see, the conventional approach to helicopter design (tail rotor, main rotor) is a pretty Heath Robinson way to solve the problem of torque induced by the main rotor. The tail rotor doesn't just counter the torque, it adds a vector in the direction the tail rotor is pulling or pushing. This tends to push the helicopter to one side, which in turn must be countered by tilt against the tail rotor by the pilot - hence conventional machines tend to move forward and hover with a sideways tilt. It's a poor solution but one that has gained acceptance.
The coaxial design is smarter - torque vs. torque, no sideways vectors. If nothing else, it's a mathematically elegant solution to a real-world problem. If you counter torque with torque you should produce the perfect flying rotorcraft, or so the theory goes. But in the real world things are never this simple. For one thing its massively more complex than the already complex CCPM design. You need more spare parts, and more complexity means more things to go wrong and more elements be maintained. There's also the problem of vibration - something that never gets mentioned in military aviation sites because most people on aviation sites don't really understand the engineering of a helicopter, only its applications. From an engineering perspective vibration plagues all rotor-based designs. Vibration in a helicopter is a massive issue even when its well-tuned, and two counter-rotating main disks are going to cause nightmares for designers. The vibration of a main rotor turning at low to mid RPMs can rip a machine apart if they're unbalanced.
Fortunately RC machines don't suffer from political machinations but real-world helicopters do. Kamov make excellent coaxial machines - arguably they've cornered the market. But they spent much of their time considered politically second-best to Mil, so the Russians didn't bother with Kamov aircraft. It offered little advantage to work with Kamov as they were less well connected politically. There are no Western manufacturers working with coaxial designs so its withered on the vine as a concept.
Does this mean that coaxial designs are the way ahead? Probably not. Coaxial designed machines are very stable, but stability is not always desirable. RC manufacturers market coaxial designs as 'beginner' or 'entry level' machines because there stability makes them slow and lacking in agility. They potter around nicely and are wonderfully stable to hang a remote camera from, but you can't stunt them and their lack of performance compared to the tail rotor design makes them feel a little tame.
Tail rotor machines can have fly-by-wire added to them to make them more stable and yet retain their inherent agility. By contrast, you can't make a stable coaxial design more agile easily. Tail rotor designs are more promising in terms of development in the same way that an unstable fighter is more promising when you add a fly-by-wire element to it.
But don't take my word for it. You can pick up a 'toy' coaxial machine for next to nothing these days. Get yourself one and see for yourself the advantages and disadvantages of coaxial vs. tail rotor design.